\batchmode


\documentclass[11pt]{article}
\RequirePackage{ifthen}


\usepackage{jair}
\usepackage{theapa}
\input epsf %


\usepackage{epsfig,latexsym}


\usepackage{graphicx}
\usepackage{graphics}
\usepackage{amsmath}
\usepackage{url}
\usepackage{mathptm}
\usepackage{longtable}
\usepackage{setspace}


\jairheading{1}{2004}{1-15}{10/04}{1/05}
\ShortHeadings{Abstract Reasoning for Planning and Coordination}
{Clement, Durfee, \& Barrett}
\firstpageno{1}


\tolerance=500

\newtheorem{definition}{Definition} 
\newtheorem{axiom}{Axiom}%
\providecommand{\ttbs}{\char'134} 

\hyphenation{author another created financial paper re-commend-ed Post-Script} 




\usepackage[dvips]{color}


\pagecolor[gray]{.7}

\usepackage[latin1]{inputenc}



\makeatletter
\AtBeginDocument{\makeatletter
\input /home/bclement/jair/jair06efinal.aux
\makeatother
}

\makeatletter
\count@=\the\catcode`\_ \catcode`\_=8 
\newenvironment{tex2html_wrap}{}{}%
\catcode`\<=12\catcode`\_=\count@
\newcommand{\providedcommand}[1]{\expandafter\providecommand\csname #1\endcsname}%
\newcommand{\renewedcommand}[1]{\expandafter\providecommand\csname #1\endcsname{}%
  \expandafter\renewcommand\csname #1\endcsname}%
\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}%
\let\newedcommand\renewedcommand
\let\renewedenvironment\newedenvironment
\makeatother
\let\mathon=$
\let\mathoff=$
\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
\newbox\sizebox
\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
\setlength{\textwidth}{349pt}
\newwrite\lthtmlwrite
\makeatletter
\let\realnormalsize=\normalsize
\global\topskip=2sp
\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float
\def\@float{\let\@savefreelist\@freelist\real@float}
\def\liih@math{\ifmmode$\else\bad@math\fi}
\def\end@float{\realend@float\global\let\@freelist\@savefreelist}
\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float
\let\@largefloatcheck=\relax
\let\if@boxedmulticols=\iftrue
\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt}
\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
 \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}%
 \def\phantompar{\csname par\endcsname}\normalsize}%
\def\lthtmltypeout#1{{\let\protect\string \immediate\write\lthtmlwrite{#1}}}%
\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }%
\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }%
\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup %
 \let\ifinner=\iffalse \let\)\liih@math }%
\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}%
 \expandafter\box\next\egroup}%
\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}%
\newcommand\lthtmllogmath{\lthtmltypeout{l2hSize %
:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist
       \lthtmlmathtype{#1}\lthtmlvboxmathA}%
\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}%
\newcommand\lthtmlpictureB[1]{\lthtmlmathtype{#1}\egroup
       \let\@savefreelist\@freelist \lthtmlhboxmathB}%
\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}%
\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
       \global\let\@freelist\@savefreelist}%
\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}%
\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
  \lthtmldisplayA{#1}\let\@eqnnum\relax}%
\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
  \vrule height1.5ex width0pt }%
\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
\newcommand\lthtmlindisplaymathZ{\egroup %
  \centerinlinemath\lthtmllogmath\lthtmlsetmath}
\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
  \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
  \kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt%
  \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt%
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
\def\centerinlinemath{%
  \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
  \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1 
 \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}

\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize 
  \ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill
  \else\expandafter\vss\fi}%
\providecommand{\selectlanguage}[1]{}%
\makeatletter \tracingstats = 1 


\begin{document}
\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}%
\makeatletter
\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}%
\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
\lthtmltypeout{}%
\makeatother
\setcounter{page}{1}
\onecolumn

% !!! IMAGES START HERE !!!

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7585}%
$equip\_M2\_tool$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7587}%
$available$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7589}%
$produce\_G$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7591}%
$calibrate\_M2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7595}%
$build\_H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7597}%
$and$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7599}%
$or$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7601}%
$MightSomeWay$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7603}%
$maintenance$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7605}%
$n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7607}%
$c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7609}%
$v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7611}%
$t1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7613}%
$p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7615}%
$p'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7617}%
$p^{-}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7619}%
${p'}^{-}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{paragraph}
\stepcounter{paragraph}
\stepcounter{paragraph}
\stepcounter{paragraph}
\stepcounter{paragraph}
\stepcounter{paragraph}
\stepcounter{paragraph}
\stepcounter{paragraph}
\stepcounter{paragraph}
\stepcounter{paragraph}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure71}%
\begin{figure}\centerline{\psfig{figure=factory2.eps,height=1.5in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1792}%
$produce\_G\_on\_M1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1794}%
$produce\_G\_on\_M2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure77}%
\begin{figure}\centerline{\psfig{figure=pm.eps,height=1.9in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1796}%
$service\_M2M1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1798}%
$service\_M1M2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure83}%
\begin{figure}\centerline{\psfig{figure=fm.eps,height=1.6in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure89}%
\begin{figure}\centerline{\psfig{figure=im.eps,height=0.9in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1800}%
$CanAnyWay$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1802}%
$\neg CanAnyWay$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1806}%
$produce\_H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1810}%
$in(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1814}%
$t_s(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1818}%
$pre(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1820}%
$post(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1824}%
$t_f(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1826}%
$res$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1828}%
$usage(p,res)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1832}%
$d(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1838}%
$order(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1840}%
$e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1844}%
$r(h,t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1846}%
$t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1848}%
$h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1850}%
$\ell$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1852}%
$\neg\ell$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1858}%
$r(res,h,t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1878}%
$\langle pre$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1880}%
$in$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1882}%
$post$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1884}%
$usage$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1886}%
$type$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1888}%
$subplans$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1890}%
$order\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1900}%
$\neg v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1908}%
$pre$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1924}%
$usage(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1926}%
$(res, amount)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1930}%
$\langle min\_value$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1932}%
$max\_value$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1934}%
$type\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1942}%
$type(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1944}%
$primitive$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1736}%
\begin{displaymath}\langle\{\}, \{\}, \{\}, \{\}, and, \{produce\_G, produce\_H\_from\_G\},
\{before(0, 1)
\}\rangle.\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1972}%
$before$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1976}%
$produce\_H\_from\_G$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1737}%
\begin{displaymath}\langle\{
\}, 
\{
\}, 
\{
\}, \{\}, and, 
\{start\_move, finish\_move\}, \{meets(0, 1)\}\rangle.\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1980}%
$meets$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1982}%
$start\_move$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1738}%
\begin{displaymath}
\begin{array}{@{}l@{}l}
\langle & \{at(A,bin1), available(A), free(transport1), \neg full(M1\_tray1)\},\\
& \{\neg at(A, bin1), \neg available(A), \neg full(bin1), \neg full(M1\_tray1), free(transport1)\},\\
& \{\neg at(A, bin1), \neg available(A), \neg free(transport1), \neg full(bin1), \neg full(M1\_tray1) \},\\
& \{\}, primitive, \{\}, \{\}\rangle.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1984}%
$finish\_move$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1739}%
\begin{displaymath}
\begin{array}{@{}l@{}l}
\langle
& \{\neg at(A, bin1), \neg available(A), \neg free(transport1), \neg full(bin1), \neg full(M1\_tray1)\}, \\
& \{\neg at(A, bin1), \neg available(A), \neg free(transport1), \neg full(bin1), full(M1\_tray1)\}, \\
& \{\neg at(A, bin1), at(A, M1\_tray1), available(A), free(transport1), \neg full(bin1), full(M1\_tray1)\}, \\
& \{\}, primitive, \{\}, \{\}\rangle.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1986}%
$\neg free$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1996}%
$move\_plan$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1998}%
$free$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2002}%
$\forall agent, agent \not=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2004}%
$\rightarrow \neg using$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2006}%
$agent$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2012}%
$\langle d, t_s, t_f\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2014}%
$t_s(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2016}%
$t_f(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2020}%
$t_s < t_f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2022}%
$d(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2036}%
$e'\in d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2038}%
$t_s(e')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2040}%
$t_f(e')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2046}%
$t_s(e')=t_s(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2050}%
$t_f(e')=t_f(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2054}%
$\mathcal{E}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2056}%
$(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2064}%
$e\in\mathcal{E}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2066}%
$(produce\_H)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2070}%
$\langle\{e_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2072}%
$e_2\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2074}%
$\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2076}%
$e_1\in\mathcal{E}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2078}%
$(produce\_G)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2080}%
$e_2\in\mathcal{E}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2082}%
$(produce\_H\_from\_G)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2088}%
$subex(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2092}%
$s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2096}%
$\langle E, s_I\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2098}%
$E$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2102}%
$s_I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2110}%
$E(h)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2118}%
$move\_parts$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2120}%
$r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1740}%
\begin{displaymath}
r(h,0) = s_I
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1741}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
v \in r(h,t>0) \Leftrightarrow &(&v \in r(h,t-\epsilon) \vee \\%\begin{array}{@{}l@{}l}
                              &&\exists p, e_p\in E(h), (v \in in(p) \wedge
                                            t_s(e_p) = t-\epsilon) \vee
                                           (v \in post(p) \wedge
                                            t_f(e_p) = t))\wedge \\
                             &(&\not\exists p', e_{p'}\in E(h), (\neg v \in in(p') \wedge
                                            t_s(e_{p'}) = t-\epsilon) \vee
                                            (\neg v \in post(p') \wedge
                                            t_f(e_{p'}) = t))
\par
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2136}%
$t+\epsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2138}%
$\epsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1742}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
r(consumable\_res,h,t) = r(consumable\_res,h,t-\epsilon) - \sum_{e_p\in E(h), t_s(e_p)=t} usage(p,consumable\_res)
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1743}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
r(nonconsumable\_res,h,t) = &r(nonconsumable\_res,h,t-\epsilon) - \\
     &\sum_{e_p\in E(h), t_s(e_p)=t} usage(p,nonconsumable\_res) + \\
     &\sum_{e_p\in E(h), t_f(e_p)=t} usage(p,nonconsumable\_res)
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1744}%
\begin{displaymath}
\begin{array}{@{}l@{}l}
succeeds(e_p, h) \equiv &pre(p) \subseteq r(h,t_s(e_p)) \wedge \\
                        &post(p) \subseteq r(h,t_f(e_p)) \wedge \\
                        &\begin{array}{@{}l@{}l}
                         \forall t, res, &t_s(e_p) < t < t_f(e_p) \wedge
                                         usage(p,res) \not = 0 \rightarrow \\
                                 &in(p) \subseteq r(h,t) \wedge \\
                                 &min\_value(res) <= r(res,h,t) <= max\_value(res) \wedge
                         \end{array} \\
                        &\forall e \in d(e_p), succeeds(e,h)
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath1745}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
asserts(e_p,\ell,t,h) \equiv &(&e_p \in E(h)) \wedge \\
                             &(&\ell \in in(p) \wedge t = t_s(e_p) + \epsilon \vee \\
                              &&\ell \in post(p) \wedge t = t_f(e_p)) \wedge \\
                              &(&r(t,h) \vdash \ell)
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2152}%
$e_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2162}%
$a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2164}%
$b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2168}%
$d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1746}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
[ach&ieves,clobbers]
\_precondition(e_p,\ell,e_{p'},t,h) \equiv \\
  &e_p, e_{p'} \in E(h) \wedge \\
  &asserts(e_p,[\ell,\neg\ell],t,h) \wedge \ell\in pre(p') \wedge t<t_s(e_{p'}) \wedge \\
  &\not\exists e_{p''}, t'', (asserts(e_{p''},\ell,t'',h) \vee asserts(e_{p''},\neg\ell,t'',h)) \wedge t<t''\leq t_s(e_{p'})
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1747}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
clob&bers\_[in,post]condition(e_p,\ell,e_{p'},t,h) \equiv \\
  &e_p, e_{p'} \in E(h) \wedge \\
  &asserts(e_p,\neg\ell,t,h) \wedge \ell\in [in(p'),post(p')] \wedge [t_s(e_{p'})<t<t_s(e_{p'}), t=t_f(e_{p'})]
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1748}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
undo&es(e_p,\ell,e_{p'},t,h) \equiv \\
  &e_p, e_{p'} \in E(h) \wedge \\
  &asserts(e_p,\neg\ell,t,h) \wedge \ell\in post(p') \wedge t_f(e_{p'})>t \wedge \\
  &\not\exists e_{p''}, t'', (asserts(e_{p''},\ell,t'',h) \vee asserts(e_{p''},\neg\ell,t'',h)) \wedge t_f(e_{p'}) \leq t'' < t
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2180}%
$e'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure310}%
\begin{figure}\centerline{\psfig{figure=interactions5.eps,height=2.8in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath1749}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
exte&rnal\_[pre,post]condition(\ell, e_p) \equiv \\
  &\exists h, E(h) = \{ e_p \} \cup subex(e_p) \rightarrow \\
  &(\exists e_{p'} \in E(h), \ell \in [pre(p'),post(p')] \wedge \\
  &\begin{array}{@{}l@{}l}
    \not\exists e_{p''} \in E(h), t, &[achieves\_pre,undoes\_post]condition(e_{p''}, \ell, e_{p'},t,h))
\end{array}
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2200}%
$available(G)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2208}%
$available(M1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2214}%
$pre_{sum}(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2216}%
$in_{sum}(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2218}%
$post_{sum}(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2220}%
$usage_{sum}(p,res)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2224}%
$consistent$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2226}%
$existence$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2228}%
$must$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2230}%
$may$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2232}%
$timing$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2234}%
$first$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2236}%
$last$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2238}%
$always$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2240}%
$sometimes$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2242}%
$p_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2244}%
$c_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2246}%
$p_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2270}%
$\langle local\_min$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2272}%
$local\_max$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2274}%
$persist \rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2278}%
$p_{sum}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2280}%
$\langle pre_{sum}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2282}%
$in_{sum}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2284}%
$post_{sum}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2286}%
$usage_{sum}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2288}%
$consistent\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2306}%
$\langle\ell,existence, timing\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2308}%
$\ell(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2320}%
$existence(c)=must$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2328}%
$must(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2334}%
$may(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2336}%
$true$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2352}%
$timing(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2356}%
$c\in in_{sum}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2364}%
$timing(c)=sometimes$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2394}%
$clobber$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2404}%
$c\in pre_{sum}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2410}%
$timing=sometimes$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2416}%
$c\in post_{sum}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2428}%
$must(c)\Rightarrow may(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2430}%
$always(c)\Rightarrow
sometimes(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1750}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
[mu&st,may]\_first\_precondition(\ell, p) \equiv \\
    &\forall p'=\langle pre(p), in(p), post(p), \{\}, type(p), subplans(p'), order(p)\rangle \wedge \\
    &\begin{array}{@{}l@{}l@{}l}
    su&mmary\ information\ of\ subplans(p')\ =\ summary\ information\ for\ subplans(p)\ \rightarrow \\
&\begin{array}{@{}l@{}l@{}l}
        \forall h, &e_{p'}, E(h) = \{ e_{p'} \} \cup subex(e_{p'}) \wedge [true, external\_precondition(\ell, e_{p'})] \rightarrow \\
&\exists e_{p''} \in E(h), t_s(e_{p''}) = t_s(e_{p'}) \wedge \ell \in pre(p'')
        \end{array}
     \end{array}
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1751}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
must&\_always\_incondition(\ell, p) \equiv \\
    &\forall p'=\langle pre(p), in(p), post(p), \{\}, type(p), subplans(p'), order(p)\rangle \wedge \\
    &\begin{array}{@{}l@{}l@{}l}
    summ&ary\ information\ of\ subplans(p')\ =\ summary\ information\ for\ subplans(p)\ \rightarrow \\
        &\begin{array}{@{}l@{}l@{}l}
        \forall h, e_{p'}, &E(h) = \{ e_{p'} \} \cup subex(e_{p'}), t, t_s(e_{p'})<t<t_f(e_{p'}) \rightarrow \\
&\exists e_{p''} \in E(h), t_s(e_{p''})<t<t_f(e_{p''}) \wedge \ell\in in(p'')
\end{array}
\end{array}
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1752}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
[mus&t,may]\_sometimes\_incondition(\ell, p) \equiv \\
    &[\forall,\exists] p'=\langle pre(p), in(p), post(p), \{\}, type(p), subplans(p'), order(p)\rangle \wedge \\
    &\begin{array}{@{}l@{}l@{}l}
    summ&ary\ information\ of\ subplans(p')\ =\ summary\ information\ for\ subplans(p)\ [\rightarrow,\wedge] \\
        &\begin{array}{@{}l@{}l@{}l}
        [\forall,\exists] h, e_{p'}, &E(h) = \{ e_{p'} \} \cup subex(e_{p'}), \exists t, t_s(e_{p'})<t<t_f(e_{p'}) [\rightarrow,\wedge] \\
&\begin{array}{@{}l@{}l@{}l}
               \exists e_{p''} \in E(h),\ &t=t_s(e_{p''}) \wedge \ell\in pre(p'') \vee \\
&t_s(e_{p''})<t<t_f(e_{p''}) \wedge \ell\in in(p'') \vee \\
&t=t_f(e_{p''}) \wedge \ell\in post(p'')
\end{array}
\end{array}
\end{array}
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2454}%
$t_s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2456}%
$t_f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2472}%
$p''$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1753}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
cons&istent(p) \equiv \\
    &\forall p'=\langle pre(p), in(p), post(p), usage(p), type(p), subplans(p'), order(p)\rangle \wedge \\
    &\begin{array}{@{}l@{}l@{}l}
    summ&ary\ information\ of\ subplans(p')\ =\ summary\ information\ for\ subplans(p)\ \rightarrow \\
        &\forall h, e_{p'} \in \mathcal{E}(p'), e_{p'} succeeds
\end{array}
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2504}%
$\neg$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2522}%
$available(A)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2526}%
$\neg available(M1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2540}%
$\neg available(A)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2544}%
$make\_G$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2556}%
$available(H)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2560}%
$available(M2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2574}%
$available(M2)MaS$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2578}%
$available(M2)MuF$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2596}%
$p_1'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2598}%
$p_2'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2606}%
$\ell(c_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1754}%
\begin{displaymath}
\begin{array}{@{}l@{}l@{}l}
must&\_[achieve,clobber]
\_precondition(p_1,c_2,p_2,P_{sum},order) \equiv \\
  &\begin{array}{@{}l@{}l@{}l}
\forall h\in &H(P_{sum},order), p_1', p_2', e_{p_1'}, e_{p_2'}, \\
            &(p_1'\ and\ p_2'\ have\ same\ summary\ and\ ordering\ information\ as\ p_1\ and\ p_2)\ \rightarrow \\
&\begin{array}{@{}l@{}l@{}l}
             \exists t, &e_{p_1''} \in subex(e_{p_1'}), e_{p_2''} \in subex(e_{p_2'}), \\
                 &[achieve,clobber]\_precondition(e_{p_1''}, \ell(c_2), e_{p_2''}, t, h)\ \wedge \\
                 &external\_precondition(\ell(c_2),e_{p_2'})
            \end{array}
        \end{array}
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2610}%
$\exists$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2612}%
$\forall$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2622}%
$c'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2628}%
$assert$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure552}%
\begin{figure}{\ttfamily
\small
\begin{tabbing}
x \= xx \= xx \= xx \= xx \= xx \= xx \= \kill
Algorithm: Must-[achieve, clobber] \\
Input: plan $p'$, summary condition $c$\  of plan $p$, $P_{sum}$, and $order$\  \\
Output: $true$\  or $false$, whether $p'$\  must-[achieve, clobber] $c$\  \\
begin function \\
\> for each $c' \in in(p') \cup post(p')$\  \\
\> \> if $\ell(c')\Leftrightarrow$\  [$\ell(c)$, $\neg\ell(c)$] $\wedge$\  $must(c')$\  then \\
\> \> \> if $c \in in_{sum}(p)$\  $\wedge$\  $p'$\  must-assert $c'$\  in $c$\  then return [$undefined$, $true$] \\
\> \> \> if $c \in post_{sum}(p)$\  $\wedge$\  $p'$\  must-assert $c'$\  when $c$\  then return [$undefined$, $true$] \\
\> \> \> if $c \in pre_{sum}(p)$\  $\wedge$\  $p'$\  must-assert $c'$\  by $c$\  then \\
\> \> \> \> set $assertion\_inbetween = false$\  \\
\> \> \> \> for each $c'' \in in(p'') \cup post(p'')$, $p'' \in P_{sum}$\  while $assertion\_inbetween = false$\  \\
\> \> \> \> \> if ($p'$\  may-assert $c'$\  before $c''$\  $\wedge$\  \\
\> \> \> \> \> \> $p''$\  may-assert $c''$\  by $c$\  $\wedge$\  \\
\> \> \> \> \> \> $\ell(c'')\Leftrightarrow$\  [$\neg\ell(c)$, $\ell(c)$]) $\vee$\  \\
\> \> \> \> \> \> ($p'$\  must-assert $c'$\  before $c''$\  $\wedge$\  \\
\> \> \> \> \> \> $p''$\  must-assert $c''$\  by $c$\  $\wedge$\  \\
\> \> \> \> \> \> $\ell(c'')\Leftrightarrow$\  [$\ell(c)$, $\neg\ell(c)$] $\wedge$\  $must(c'')$) then \\
\> \> \> \> \> \> \> set $assertion\_inbetween = true$\  \\
\> \> \> \> if $\neg assertion\_inbetween$\  then return $true$\  \\
\> return $false$\  \\
end function
\end{tabbing}
}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure563}%
\begin{figure}{\ttfamily
\small
\begin{tabbing}
x \= xx \= xx \= xx \= xx \= xx \= xx \= \kill
Algorithm: May-[achieve, clobber] \\
Input: plan $p'$, summary condition $c$\  of plan $p$\  \\
Output: $true$\  or $false$, whether $p'$\  may-[achieve, clobber] $c$\  \\
begin function \\
\> for each $c' \in in(p') \cup post(p')$\  \\
\> \> if $\ell(c')\Leftrightarrow$\  [$\ell(c)$, $\neg\ell(c)$] then \\
\> \> \> if $c \in in_{sum}(p)$\  $\wedge$\  $p'$\  may-assert $c'$\  in $c$\  then return [$undefined$, $true$] \\
\> \> \> if $c \in post_{sum}(p)$\  $\wedge$\  $p'$\  may-assert $c'$\  when $c$\  then return [$undefined$, $true$] \\
\> \> \> if $c \in pre_{sum}(p)$\  $\wedge$\  $p'$\  may-assert $c'$\  by $c$\  then \\
\> \> \> \> set $assertion\_inbetween = false$\  \\
\> \> \> \> for each $c'' \in in(p'') \cup post(p'')$, $p'' \in P_{sum}$\  while $assertion\_inbetween = false$\  \\
\> \> \> \> \> if $p'$\  must-assert $c'$\  before $c''$\  $\wedge$\  \\
\> \> \> \> \> \> $p''$\  must-assert $c''$\  by $c$\  $\wedge$\  \\
\> \> \> \> \> \> $\ell(c'')\Leftrightarrow$\  $\ell(c)$\  or $\neg\ell(c)$\  $\wedge$\  $must(c'')$) then \\
\> \> \> \> \> \> \> set $assertion\_inbetween = true$\  \\
\> \> \> \> if $\neg assertion\_inbetween$\  then return $true$\  \\
\> return $false$\  \\
end function
\end{tabbing}
}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2866}%
$O(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2874}%
$c''$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2876}%
$O(nc)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2882}%
$P_{sum}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2886}%
$p' = equip\_M2\_tool$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2892}%
$p = produce\_G$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2902}%
$p' = build\_H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2908}%
$p = move\_H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2920}%
$move\_H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2936}%
$\neg available$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure578}%
\begin{figure}\centerline{\psfig{figure=assert2.eps,height=3.0in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2988}%
$x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2990}%
$y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure587}%
\begin{figure}
% latex2html id marker 587
{\ttfamily
\small
\begin{tabbing}
x \= xx \= xx \= xx \= xx \= xx \= xx \= \kill
Algorithm: Derive summary information \\
Input: plan $p$\  \\
Output: $p_{sum}$\  \\
begin function \\
\> derive summary information for each $p'\in d(p)$\\
\> set $consistent(p)$\  = $\bigwedge_{p'\in d(p)} consistent(p')$\  \\
\> for each $\ell\in pre(p)$\  add $\langle \ell, must, first\rangle$\  to $pre_{sum}(p)$\  \\%end for \\
\> for each $\ell\in in(p)$\  add $\langle \ell, must, always\rangle$\  to $in_{sum}(p)$\  \\%end for \\
\> for each $\ell\in post(p)$\  add $\langle \ell, must, last\rangle$\  to $post_{sum}(p)$\  \\%end for \\
\> for each summary condition $c'$\  of $p'\in d(p)$\  \\
\> \> set $c$\  = $c'$\  \\
\> \> if $c' \in$\  \{$pre_{sum}(p')$,$post_{sum}(p')$\} and \\
\> \> \> $c'$\  is not $must$-\{$achieved$,$undone$\} or $must$-$clobbered$\  within $d(p)$, then\\
\> \> \> if $type(p)=and$\  and ($p'$\  is \emph{always not} the \{$first$,$last$\} \\
\> \> \> \> temporally ordered subplan according to $order(p)$\  or \\
\> \> \> \> there is a \emph{sometimes-}\{$first$,$last$\} subplan $p'$\  that \\
\> \> \> \> does not have a \{$first$, $last$\} $\ell(c')$\  condition in \{$pre_{sum}(p')$,$post_{sum}(p')$\}), then \\
\> \> \> \> set $timing(c)$\  = $sometimes$\  \\
\> \> \> if $c'$\  is $may$-\{$achieved$,$undone$\} or $may$-$clobbered$\  by each of $P\subset d(p)$\  and \\
\> \> \> \> not all $p''\in P$\  have a $must$\  $\ell(c')$\  condition in \{$pre_{sum}(p'')$,$post_{sum}(p'')$\}, then \\
\> \> \> \> set $existence(c)$\  = $may$\  \\
\> \> \> copy $c$\  to \{$pre_{sum}(p)$,$post_{sum}(p)$\} \\
\> \> if $c' \in in_{sum}(p')$\  or $p'$\  is \emph{not-always}\{$first$,$last$\} according to $order(p)$, then \\
\> \> \> if $must(c')$\  and $c'$\  is \emph{always-not-}\{$first$,$last$\} according to $order(p)$, then \\
\> \> \> \> set $existence(c)$\  = $must$\  \\
\> \> \> set $P=\emptyset$\  \\
\> \> \> set $allAlways = true$\  \\
\> \> \> for each $p''\in d(p),c''\in in_{sum}(p'')$\  \\
\> \> \> \> if $\ell(c'') \Leftrightarrow \ell(c)$\  \\
\> \> \> \> \> if $always(c'')$\  then add $p''$\  to $P$\  \\
\> \> \> \> \> else set $allAlways$\  = $false$\  \\%end if\\
\> \> \> \> else $allAlways=false$\  \\%end if \\
\> \> \> if $always(c)$\  and (($type(p)=and$\  and $P$\  $covers$\  $p$\  according to $order(p)$) or\\
\> \> \> \> ($type(p)=or$\  and $allAlways$)), then \\
\> \> \> \> set $timing(c)$\  = $always$\  \\
\> \> \> add $c$\  to $in_{sum}(p)$\  \\
\> \> if $c'$\  is $may$-$clobbered$, then set $consistent=false$\  \\
\> $usage_{sum}(p)$\  = SummarizeResourceUsage($p$) (in Section~\ref{sec:ressumm}) \\
\> if $consistent(usage_{sum}(p)) = false$, then set $consistent(p) = false$\  \\
end function
\end{tabbing}
}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlfigureA{figure623}%
\begin{figure}\centerline{\psfig{figure=map1.eps,height=1.1in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3220}%
$A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3222}%
$B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure632}%
\begin{figure}\centerline{\psfig{figure=activities.eps,height=1.3in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1755}%
\begin{displaymath}usage_{sum}(p, res) = \langle local\_min(p,res),local\_max(p,res),persist(p,res)\rangle,\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1756}%
\begin{displaymath}
\setlength{\arraycolsep}{0in} 
\begin{array}[t]{lll}
usage_{sum}(p, res) \equiv \\
   \begin{array}[t]{llllll}
   \langle   & [ & min_{h\in H, e_p\in E(h)}(min_{t_s(e_p)<t<t_f(e_p)}(-r(res,h,t))),\ 
                 & max_{h\in H, e_p\in E(h)}(min_{t_s(e_p)<t<t_f(e_p)}(-r(res,h,t)))] \\
             & [ & min_{h\in H, e_p\in E(h)}(max_{t_s(e_p)<t<t_f(e_p)}(-r(res,h,t))),\ 
                 & max_{h\in H, e_p\in E(h)}(max_{t_s(e_p)<t<t_f(e_p)}(-r(res,h,t)))] \\
             & [ & min_{h\in H, e_p\in E(h)}(-r(res,h,t_f(e_p))),\ 
                 & max_{h\in H, e_p\in E(h)}(-r(res,h,t_f(e_p)))]&   \rangle
\end{array}
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3238}%
$H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3246}%
$-r(res,h,t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3252}%
$local\_min$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3256}%
$\langle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3260}%
$move$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3266}%
$persist$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3278}%
$\langle[x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3280}%
$x]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3282}%
$[x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3286}%
$[0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3288}%
$0]\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3300}%
$x]\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1757}%
\begin{displaymath}
\setlength{\arraycolsep}{0in} 
\begin{array}[t]{lllll}
\langle\ & [ & min_{c \in children}(lb(local\_min(c))),\ 
             & max_{c \in children}(ub(local\_min(c)))],\\
& [ & min_{c \in children}(lb(local\_max(c))),\ 
    & max_{c \in children}(ub(local\_max(c)))],\\
& [ & min_{c \in children}(lb(persist(c))),\ 
    & max_{c \in children}(ub(persist(c)))]&\ \rangle,
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3314}%
$lb()$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3316}%
$ub()$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3318}%
$children$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1758}%
\begin{displaymath}
\setlength{\arraycolsep}{0in} 
\begin{array}[t]{lllll}
\langle\ & [ & min_{c \in children}(lb(local\_min(c))+\Sigma_{lb}^{pre}(c)),\ 
             & min_{c \in children}(ub(local\_min(c))+\Sigma_{ub}^{pre}(c))],\\
& [ & max_{c \in children}(lb(local\_max(c))+\Sigma_{lb}^{pre}(c)),\ 
    & max_{c \in children}(ub(local\_max(c))+\Sigma_{ub}^{pre}(c))],\\
& [ & \Sigma_{c \in children}(lb(persist(c))),\ 
    & \Sigma_{c \in children}(ub(persist(c)))] & \ \rangle,\\
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3330}%
$\Sigma_{lb}^{pre}(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3332}%
$\Sigma_{ub}^{pre}(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3336}%
$\Sigma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1759}%
\begin{displaymath}
\setlength{\arraycolsep}{0in} 
\begin{array}[t]{lllll}
\langle\ & [ & \Sigma_{c \in children}(lb(local\_min(c))),\ 
            & max_{c \in children}(ub(local\_min(c))+\Sigma_{ub}^{non}(c))],\\
& [ & min_{c \in children}(lb(local\_max(c))+\Sigma_{lb}^{non}(c)),\ 
    & \Sigma_{c \in children}(ub(local\_max(c)))],\\
& [ & \Sigma_{c \in children}(lb(persist(c))),\ 
    & \Sigma_{c \in children}(ub(persist(c)))] & \ \rangle,\\
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3340}%
$\Sigma_{ub}^{non}(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3342}%
$\Sigma_{lb}^{non}(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure724}%
\begin{figure}\centerline{\psfig{figure=taskorder1.eps,height=1.0in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3360}%
$\langle[a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3362}%
$b]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3364}%
$[c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3366}%
$d]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3368}%
$[e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3370}%
$f]\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3372}%
$[0,0]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3374}%
$[e,f]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1760}%
\begin{displaymath}
\langle[a,b],[c,d],[0,0]\rangle,\langle[a,d],[a,d],[0,0]\rangle.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3404}%
$m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3408}%
$n^{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3420}%
$P$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3422}%
$order$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3424}%
$p\in P$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3428}%
$p'\in P$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3438}%
$must(c')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3448}%
$O(n^2c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3452}%
$\neg MightSomeWay$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1761}%
\begin{displaymath}
\begin{array}{@{}l@{}l}
[CanAnyWay&,MightSomeWay](order, P_{sum}) \equiv \\
    &[\forall, \exists] h, P\ with\ summary\ information\ =\ P_{sum} \wedge h\in H(P,order) \rightarrow \\
    &[\forall, \exists] e \in E(h), succeeds(e,h)
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3466}%
$CanSomeWay(order$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3468}%
$P_{sum})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3470}%
$MightAnyWay(rel$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure769}%
\begin{figure}\centerline{\psfig{figure=cawmsw3.eps,height=2.7in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure774}%
\begin{figure}
% latex2html id marker 774
{\ttfamily
\small
\begin{tabbing}
x \= xx \= xx \= xx \= xx \= xx \= xx \= \kill
Algorithm: [$CanAnyWay$, $MightSomeWay$] \\
Input: $order$, $P_{sum}$\  \\
Output: $true$\  or $false$\  \\
begin function \\
\> for each  $p_{sum}\in P_{sum}$\  \\
\> \> if [$\neg consistent(p_{sum})$, $false$] then return $false$\  \\
\> \> for each  $p_{sum}'\in P_{sum}$\  \\
\> \> \> for each summary condition $c$\  of $p_{sum}$\  \\
\> \> \> \> if $p'$\  [may-clobber, must-clobber] $c$, and \\
\> \> \> \> \> \> $c$\  is [$may$\  or $must$, $must$], then \\
\> \> \> \> \> return $false$\  \\
\> for each resource $res$\  \\
\> \> if $\neg$[$CanAnyWay$, $MightSomeWay$]$(order,P_{sum},res)$\  (see Section \ref{sec:rescon}) then \\
\> \> \> return false \\
\> return $true$\  \\
end function
\end{tabbing}
}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3590}%
$false$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure793}%
\begin{figure}\centerline{\psfig{figure=notcomplete.eps,height=1.0in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3606}%
$nc$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3648}%
$CanAnyWay(order, P_{sum}, res)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3650}%
$i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1762}%
\begin{displaymath}
\setlength{\arraycolsep}{0in} 
\begin{array}[t]{lllll}
lb(local\_min(i)) < min\_value(res)\ \vee \ lb(persist(i)) < min\_value(res) \ \vee\\
ub(local\_max(i)) > max\_value(res)\ \vee \ ub(persist(i)) > max\_value(res).
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3652}%
$MightSomeWay(order, P_{sum}, res)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1763}%
\begin{displaymath}
\setlength{\arraycolsep}{0in} 
\begin{array}[t]{lllll}
ub(local\_min(i)) \geq min\_value(res)\ \wedge \ lb(persist(i)) \geq min\_value(res)\ \wedge\\
lb(local\_max(i)) \leq max\_value(res)\ \wedge \ ub(persist(i)) \leq max\_value(res).
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3664}%
$queue$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure835}%
\begin{figure}{\ttfamily
\small
\begin{tabbing}
x \= xx \= xx \= xx \= xx \= xx \= xx \= \kill
Concurrent Hierarchical Coordination Algorithm \\
Input: set of top-level $plans$, $initial\_state$\\
Output: set of $solutions$, each a pair of $order$\  constraints and $blocked$\  plan choices\\
begin function \\
\> $summarized\_plans$\  = $\emptyset$\                                                                              \\
\> for each plan $p \in plans$\                                           				     \\
\> \> $p'$\  = get summary information for plan $p$\         				     \\
\> \> $summarized\_plans$\  = $summarized\_plans$\  $\cup$\  \{ $p'$\  \}                         				     \\
\> end for   							 				     \\
\> $threats$\  = \{ ($p$, $p'$) $\mid$\  $p,p'\in summarized\_plans$, MayClobber($p$, $p'$) \}                                      				     \\
\> $queue$\  = \{ ($\emptyset$, $\emptyset$, $threats$) \}             				     \\
\> $solutions$\  = $\emptyset$\                                      				     \\
\> loop                                                          				     \\
\> \> if $queue$\  == $\emptyset$\                                   				     \\
\> \> \> return $solutions$\                                       				     \\
\> \> ($order$, $blocked$, $threats$) = Pop($queue$)               				     \\
\> \> if CanAnyWay($initial\_state$, $summarized\_plans$, $order$, $blocked$) 				     \\
\> \> \> $solution$\  = ($order$, $blocked$)              				     \\
\> \> \> $solutions$\  = $solutions$\  $\cup$\  \{$solution$\}      				             \\
\> \> \> for each $sol_1$\  and $sol_2$\  in $solutions$\                                                  				     \\
\> \> \> \> if Dominates($sol_1$, $sol_2$)          				                    \\
\> \> \> \> \> $solutions$\  = $solutions$\  - \{ $sol_2$\  \}                                              \\
\> \> if MightSomeWay($initial\_state$, $summarized\_plans$, $order$, $blocked$)				     \\
\> \> \> $operator$\  = Choose(\{expand, select, block, constrain\})				     \\
\> \> \> $queue$\  = $queue$\  $\cup$\  ApplyOperator($operator$, $summarized\_plans$, $order$, $blocked$) \\%(see Figure~\ref{fig:subalg}) \\
\> return $solutions$\     \\
end function
\end{tabbing}
}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3810}%
$plans$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3820}%
$operator$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure856}%
\begin{figure}\centerline{\psfig{figure=emtf_ex.eps,height=2.6in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3872}%
$O(bs)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3880}%
$O(b^2s^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3884}%
$s=c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3888}%
$d-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3896}%
$c+bc$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3898}%
$s=O(bc)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3900}%
$s=O(b^{d-i}c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3908}%
$i+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3910}%
$O(b^2b^{2(d-(i+1))}c^2)=O(b^{2(d-i)}c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3912}%
$b^i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3918}%
$O(b^ib^{2(d-i)}c^2)=O(b^{2d-i}c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3920}%
$O(\sum_{i=0}^{d-1} b^i b^{2(d-i)}c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3922}%
$i=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3924}%
$O(b^{2d}c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3926}%
$n=O(b^d)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3932}%
$O(\sum_{i=0}^{d-1} b^i b^2c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3934}%
$O(b^{d+1}c^2) = O(nbc^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3940}%
$O(n^2s^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3946}%
$n=O(b^i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3952}%
$O(b^{2i}(b^{d-i}c)^2)=O(b^{2d}c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3958}%
$O(b^{2i}c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3960}%
$O(b^{2(d-i)})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure904}%
\begin{figure}\centerline{\psfig{figure=kcomplexity.eps,height=3.0in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3962}%
$O(k^{b^i})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3968}%
$k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3970}%
$O(k^{b^i} b^{2d}c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3972}%
$O(k^{b^i} b^{2i}c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3974}%
$O(k^{b^d} b^{2d}c^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3976}%
$O(k^{b^d-b^i})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3978}%
$O(k^{b^d-b^i} b^{2(d-i)})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3984}%
$O(k^{(b-p)^d})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3986}%
$p/b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure931}%
\begin{figure}\centerline{\psfig{figure=compsched.eps,height=1.9in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4004}%
$O(cC)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4008}%
$C$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4012}%
$C=(n-1)c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4014}%
$O(nc^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4018}%
$O(vnc^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4020}%
$O(tnr)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4022}%
$nr$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4024}%
$t-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4030}%
$O(b^d)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4036}%
$O(vnb^{2d})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4038}%
$c=O(b^d)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4042}%
$O(b^i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4044}%
$c=O(b^i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4046}%
$O(vnb^{2i})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4054}%
$O(k^{b^{d-i}}b^{2(d-i)})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4056}%
$c=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4058}%
$v=O(b^d)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4060}%
$O(nb^d)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4072}%
$k^{b^d-b^i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4082}%
$expand$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4086}%
$select$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure986}%
\begin{figure}\centerline{\psfig{figure=ring.eps,height=1.4in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4100}%
$t2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4102}%
$s0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4104}%
$s3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4106}%
$evacuate$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4112}%
$make\ rounds$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4118}%
$first\ route$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4120}%
$second\ route$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4122}%
$go\ back$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4124}%
$goto\ safe\ loc$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4126}%
$no\ move$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure993}%
\begin{figure}\centerline{\psfig{figure=neoplan.eps,height=2.9in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure998}%
\begin{figure}\centerline{\psfig{figure=emtf_vs_rand_06_2.eps,height=2.5in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1003}%
\begin{figure}\centerline{\psfig{figure=emtf_vs_excon_06_7.eps,height=2.5in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1026}%
\begin{figure}\centerline{\psfig{figure=cftf_vs_dfs_06.eps,height=2.5in,angle=270}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1055}%
\begin{figure}\centerline{\psfig{figure=summ_vs_faf_06_2.eps,height=2.5in,angle=270}}

\vspace{10pt}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1061}%
\begin{figure}\centerline{\psfig{figure=summ_vs_excon_06_3.eps,height=2.5in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsubsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlfigureA{figure1096}%
\begin{figure}\centerline{\psfig{figure=rectfield.eps,height=1.1in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1101}%
\begin{figure}\centerline{\psfig{figure=corridor.eps,height=1.1in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlfigureA{figure1120}%
\begin{figure}\begin{center}
\begin{tabular}{c@{\hspace{7pt}}c}
\psfig{figure=no_channel_06.eps,height=2.45in,angle=270} \\
a) \\
\psfig{figure=mixed_06.eps,height=2.45in,angle=270} \\
 b) \\
\end{tabular}
\begin{tabular}{c}
\psfig{figure=channel_only_06.eps,height=2.45in,angle=270}\\
c)
\end{tabular}
\end{center}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1159}%
\begin{figure}\centerline{\psfig{figure=ftf_06.eps,height=2.7in,angle=270}}

\vspace{13pt}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1168}%
\begin{figure}\centerline{\psfig{figure=emtf2.eps,height=2.7in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{tabular1186}%
\begin{tabular}{|l|r|r|} \hline
& number of messages & total size (bytes) \\\hline
one task at a time & 9 & 8708 \\\hline
two levels at a time & 4 & 10525 \\\hline
all at once & 3 & 16268 \\\hline
\end{tabular}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1190}%
\begin{figure}\begin{center}
\begin{tabular}{@{}c@{\ }c c@{\ }c@{}}
a) \\\psfig{figure=lat1.eps,height=2.7in,angle=270} \\
b) \\\psfig{figure=bw1.eps,height=2.7in,angle=270} \\
\end{tabular}
\end{center}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4182}%
$(n-2)\ell + s/b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4192}%
$n-2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4198}%
$3\ell$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{tabular1207}%
\begin{tabular}{|l|r|r|} \hline
& number of messages & total size \\\hline
one task at a time & $O(b^i)$\  & $O(b^i)$\  \\\hline
two levels at a time & $3i/2$\  & $O(b^i)$\  \\\hline
all at once & 3 & $O(b^d)$\  \\\hline
\end{tabular}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4220}%
$i=5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{tabular1212}%
\begin{tabular}{|l|r|r|} \hline
& number of messages & total size (Kbytes) \\\hline
one task at a time & 363 & 1089 \\\hline
two levels at a time & 9 & 3276 \\\hline
all at once & 3 & 246033 \\\hline
\end{tabular}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1216}%
\begin{figure}\begin{center}
\begin{tabular}{c@{\ }c c@{\ }c}
a) \\\psfig{figure=lat2.eps,height=2.6in,angle=270} \\
b) \\\psfig{figure=bw2.eps,height=2.6in,angle=270} 
\\
\end{tabular}
\end{center}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4248}%
$p^{-} \equiv t_s(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4254}%
$p^{+} \equiv t_f(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4258}%
$<$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4260}%
$\leq$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4262}%
$=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4264}%
$\geq$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4266}%
$>$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4268}%
$\neq$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4270}%
$<=>$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4286}%
$p^{+}<{p'}^{+}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4290}%
$p^{+}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4292}%
${p'}^{+}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4294}%
$O(n^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{tabular1333}%
\begin{tabular}{|c|c|c|c|c|} \hline
           & $p^{-}$\  & $p^{+}$\  & ${p'}^{-}$\  & ${p'}^{+}$\  \\\hline
$p^{-}$\     & $=$\      & $<$\      & $<$\         & $<$\         \\\hline
$p^{+}$\     & $>$\      & $=$\      & $>$\         & $>$\         \\\hline
${p'}^{-}$\  & $>$\      & $<$\      & $=$\         & $<$\         \\\hline
${p'}^{+}$\  & $>$\      & $<$\      & $>$\         & $=$\         \\\hline
\end{tabular}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{tabular1354}%
\begin{tabular}{|c|c|c|c|c|} \hline
           & $p^{-}$\  & $p^{+}$\  & ${p'}^{-}$\  & ${p'}^{+}$\  \\\hline
$p^{-}$\     & $=$\      & $<$\      & $\leq$\      & $<$\         \\\hline
$p^{+}$\     & $>$\      & $=$\      & $<=>$\       & $<=>$\       \\\hline
${p'}^{-}$\  & $\geq$\   & $<=>$\    & $=$\         & $<$\       \\\hline
${p'}^{+}$\  & $>$\      & $<=>$\    & $>$\         & $=$\         \\\hline
\end{tabular}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4412}%
$achieve$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4416}%
$q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4424}%
$q^{-}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4426}%
$q^{+}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4468}%
$i_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4470}%
$I=\{i_1,i_2,\ldots,i_k\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4474}%
$I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4482}%
$i_0^{-}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4484}%
$i_0^{+}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1389}%
\begin{figure}\centerline{\psfig{figure=covered.eps,height=1.8in}}

\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4520}%
$conds$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4528}%
$\ell=\ell(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4536}%
$p=p'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4548}%
$at$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4582}%
$first(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4584}%
$t=t_s(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4586}%
$last(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4588}%
$t=t_f(e)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4590}%
$always(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4594}%
$(t_s(e),
t_f(e))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4596}%
$sometimes(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4614}%
$build\_G$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4648}%
$\neg first(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4698}%
$equip\_M1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{tabular1430}%
\begin{tabular}{|r|c|c|c|c|} \hline
&  &  & $p'$\  must-assert $c'$\  by $c$\  & $p'$\  must-assert $c'$\  before $c$\  \\\hline
& & & $order$\  must impose & $order$\  must impose \\
& $c' \in post(p')$\  & $c \in pre(p)$\  & these constraints & these constraints \\\hline
& $last$\  & $first$\  &  &  \\\hline
1 & T & T & ${p'}^+ \leq p^-$\  & ${p'}^+ < p^-$\  \\\hline
2 & T & F & ${p'}^+ \leq p^-$\  & ${p'}^+ < p^-$\  \\\hline
3 & F & ? & ${p'}^+ \leq p^-$\  & ${p'}^+ < p^-$\  \\\hline
4 & ? & ? & ${p'}^+ \leq p^-$\  & ${p'}^+ < p^-$\  \\\hline
& $c' \in in(p')$\  &  &  &  \\\hline
& $always$\  &  &  &  \\\hline
5 & T & T & ${p'}^- < p^-$\  & ${p'}^- < p^-$\  \\\hline
6 & T & F & ${p'}^- \leq p^-$\  & ${p'}^- \leq p^-$\  \\\hline
7 & F & ? & $false$\  & $false$\  \\\hline
& $c' \in post(p')$\  & $c \in in(p)$\  &  &  \\\hline
& $last$\  & $always$\  &  &  \\\hline
8 & T & ? & ${p'}^+ \leq p^-$\  & ${p'}^+ \leq p^-$\  \\\hline
9 & F & ? & ${p'}^+ \leq p^-$\  & ${p'}^+ \leq p^-$\   \\\hline
& $c' \in in(p')$\  &  &  & \\\hline
& $always$\  &  &  & \\\hline
10 & T & ? & ${p'}^- \leq p^-$\  & ${p'}^- < p^-$\  \\\hline
11 & F & ? & $false$\  & $false$\  \\\hline
& $c' \in post(p')$\  & $c \in post(p)$\  &  & \\\hline
& $last$\  & $last$\  &  & \\\hline
12 & T & T & ${p'}^+ \leq p^+$\  & ${p'}^+ < p^+$\  \\\hline
13 & T & F & ${p'}^+ \leq p^-$\  & ${p'}^+ \leq p^-$\  \\\hline
14 & F & T & ${p'}^+ \leq p^+$\  & ${p'}^+ \leq p^+$\  \\\hline
15 & F & F & ${p'}^+ \leq p^-$\  & ${p'}^+ \leq p^-$\  \\\hline
& $c' \in in(p')$\  &  &  & \\\hline
& $always$\  &  &  & \\\hline
16 & T & T & ${p'}^- < p^+$\  & ${p'}^- < p^+$\  \\\hline
17 & T & F & ${p'}^- \leq p^-$\  & ${p'}^- \leq p^-$\  \\\hline
18 & F & T & $false$\  & $false$\  \\\hline
19 & F & F & $false$\  & $false$\  \\\hline
\end{tabular}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{tabular1469}%
\begin{tabular}{|r|c|c|c|c|} \hline
&  &  & $p'$\  may-assert $c'$\  by $c$\  & $p'$\  may-assert $c'$\  before $c$\  \\\hline
& & & $order$\  cannot impose & $order$\  cannot impose \\
& $c' \in post(p')$\  & $c \in pre(p)$\  & these constraints & these constraints \\\hline
& $last$\  & $first$\  &  & \\\hline
1 & T & T & ${p'}^+ > p^-$\  & ${p'}^+ \geq p^-$\  \\\hline
2 & T & F & ${p'}^+ \geq p^+$\  & ${p'}^+ \geq p^+$\  \\\hline
3 & F & T & ${p'}^- \geq p^-$\  & ${p'}^- \geq p^-$\  \\\hline
4 & F & F & ${p'}^- \geq p^+$\  & ${p'}^- \geq p^+$\  \\\hline
& $c' \in in(p')$\  &  &  & \\\hline
& $always$\  &  &  & \\\hline
5 & ? & T & ${p'}^- \geq p^-$\  & ${p'}^- \geq p^-$\  \\\hline
6 & ? & F & ${p'}^- \geq p^+$\  & ${p'}^- \geq p^+$\  \\\hline
& $c' \in post(p')$\  & $c \in in(p)$\  &  & \\\hline
& $last$\  & $always$\  &  & \\\hline
7 & T & T & ${p'}^+ > p^-$\  & ${p'}^+ > p^-$\  \\\hline
8 & T & F & ${p'}^+ \geq p^+$\  & ${p'}^+ \geq p^+$\  \\\hline
9 & F & T & ${p'}^- \geq p^-$\  & ${p'}^- \geq p^-$\  \\\hline
10 & F & F & ${p'}^- \geq p^+$\  & ${p'}^- \geq p^+$\  \\\hline
& $c' \in in(p')$\  &  &  &  \\\hline 
& $always$\  &  &  &  \\\hline
11 & ? & T & ${p'}^- > p^-$\  & ${p'}^- \geq p^-$\  \\\hline
12 & ? & F & ${p'}^- \geq p^+$\  & ${p'}^- \geq p^+$\  \\\hline
& $c' \in post(p')$\  & $c \in post(p)$\  &  &  \\\hline
& $last$\  & $last$\  &  &  \\\hline
13 & T & T & ${p'}^+ > p^+$\  & ${p'}^+ \geq p^+$\  \\\hline
14 & T & F & ${p'}^+ \geq p^+$\  & ${p'}^+ \geq p^+$\  \\\hline
15 & F & T & ${p'}^- \geq p^+$\  & ${p'}^- \geq p^+$\  \\\hline
16 & F & F & ${p'}^- \geq p^+$\  & ${p'}^- \geq p^+$\  \\\hline
& $c' \in in(p')$\  &  &  &  \\\hline
& $always$\  &  &  &  \\\hline
17 & ? & T & ${p'}^- \geq p^+$\  & ${p'}^- \geq p^+$\  \\\hline
18 & ? & F & ${p'}^- \geq p^+$\  & ${p'}^- \geq p^+$\  \\\hline
\end{tabular}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{tabular1514}%
\begin{tabular}{|r|c|c|c||c|c|c|} \hline
&  &  & $p'$\  must-assert $c'$\  in $c$\                     &  &  & $p'$\  may-assert $c'$\  in $c$\   \\\hline                    
& & & $order$\  must impose                               & & & $order$\  cannot impose \\
& $c' \in post(p')$\  & $c \in in(p)$\  & these constraints & $c' \in post(p')$\  & $c \in in(p)$\  & these constraints \\\hline 
& $last$\  & $always$\  &                                   & $last$\  & $always$\  & \\\hline                                   
1 & T & T & ${p'}^+ > p^-$\  and ${p'}^+ < p^+$\            & T & T & ${p'}^+ \leq p^-$\  or ${p'}^+ \geq p^+$\  \\\hline      
2 & T & F & $false$\                                      & T & F & ${p'}^+ \leq p^-$\  or ${p'}^+ \geq p^+$\  \\\hline      
3 & F & T & ${p'}^- \geq p^-$\  and ${p'}^+ \leq p^+$\      & F & T & ${p'}^+ \leq p^-$\  or ${p'}^- \geq p^+$\  \\\hline      
4 & F & F & $false$\                                      & F & F & ${p'}^+ \leq p^-$\  or ${p'}^- \geq p^+$\  \\\hline      
& $c' \in in(p')$\  &  &                                  & $c' \in in(p')$\  &  & \\\hline                                  
& $always$\  &  &                                         & $always$\  &  &  \\\hline                                        
5 & T & T & ${p'}^- \geq p^-$\  and ${p'}^- < p^+$\         & T & T & ${p'}^+ \leq p^-$\  or ${p'}^- \geq p^+$\  \\\hline      
6 & T & F & $false$\                                      & T & F & ${p'}^+ \leq p^-$\  or ${p'}^- \geq p^+$\  \\\hline      
7 & F & T & $false$\                                      & F & T & ${p'}^+ \leq p^-$\  or ${p'}^- \geq p^+$\  \\\hline      
8 & F & F & $false$\                                      & F & F & ${p'}^+ \leq p^-$\  or ${p'}^- \geq p^+$\  \\\hline      
\end{tabular}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{tabular1545}%
\begin{tabular}{|r|c|c|c||c|c|c|} \hline
&  &  & $p'$\  must-assert $c'$\  when $c$\                        & & & $p'$\  may-assert $c'$\  when $c$\  \\\hline             
& & & $order$\  must impose                                    & & & $order$\  cannot impose \\
& $c' \in post(p')$\  & $c \in post(p)$\  & these constraints    & $c' \in post(p')$\  & $c \in post(p)$\  & these constraints \\\hline
& $last$\  & $last$\  &                                          & $last$\  & $last$\  & \\\hline                               
1 & T & T & ${p'}^+ = p^+$\                                    & T & T & ${p'}^+ \not= p^+$\  \\\hline                    
2 & T & F & $false$\                                           & T & F & ${p'}^+ \leq p^-$\  or ${p'}^+ \geq p^+$\  \\\hline
3 & F & T & $false$\                                           & F & T & ${p'}^+ \leq p^+$\  or ${p'}^- \geq p^+$\  \\\hline
4 & F & F & $false$\                                           & F & F & ${p'}^+ \leq p^-$\  or ${p'}^- \geq p^+$\  \\\hline
\end{tabular}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5116}%
$h\in H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5136}%
$t'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5144}%
$t'\leq t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5146}%
$t'<t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5162}%
$\neg last$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5190}%
$c' = must$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5196}%
$c = must$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5202}%
$move\_G$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5224}%
$c =
may$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5236}%
$equip\_M2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5240}%
$move\_tool$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
