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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5040}%
$ O_2\ll O_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5044}%
$ O_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5053}%
$ p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5055}%
$ b_1\oplus\ldots\oplus b_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5057}%
$ b_1,\ldots,b_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5059}%
$ P=b_1\oplus\ldots\oplus b_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5061}%
$ f_P: \mathds{B}\mapsto\mathds{N}: b\rightarrow f_P(b)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5065}%
$ \mathds{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5067}%
$ f_P(b)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5069}%
$ b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5073}%
$ P_{\text{model}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5081}%
$\displaystyle P_{\text{model}}=b_{21}\oplus b_{21}\oplus b_{21}\oplus b_{13}\oplus b_{13}\oplus b_{31}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5083}%
$\displaystyle f_{P_{\text{model}}}(b)=   \begin{cases}     3 & \text{if }b=b_{21}\\2 & \text{if }b=b_{13}\\1 & \text{if }b=b_{31}\\0 & \text{otherwise}   \end{cases}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5085}%
$ P_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5087}%
$ P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5089}%
$ P_1\oplus P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5091}%
$\displaystyle f_{P_1\oplus P_2}:\mathds{B}\mapsto\mathds{N}:b\rightarrow f_{P_1\oplus P_2}(b)=f_{P_1}(b)+f_{P_2}(b)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5095}%
$ P\prec P\oplus P$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5100}%
$ =$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5102}%
$ \prec$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5104}%
$ \succ$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5106}%
$ ?$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5108}%
$ \{b_1,b_2,\ldots,b_n\}\subseteq O_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5110}%
$ b\in O_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5112}%
$ O_1\ll O_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5114}%
$\displaystyle b_1\oplus b_2\oplus\ldots\oplus b_n\prec b$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5118}%
$ O_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5120}%
$ b_1,\ldots, b_{m-1},
b_m,\ldots,b_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5124}%
$ \{b,b'\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5128}%
$ b<b'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5132}%
$\displaystyle b_1\oplus\ldots\oplus b_{m-1}\oplus b\prec b_m\oplus\ldots\oplus b_n\oplus b'$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5136}%
$ b_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5138}%
$ b_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5140}%
$ b_1<b_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5144}%
$\displaystyle b_1\oplus P\prec b_2\oplus P$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5146}%
$\displaystyle b_{11}\oplus b_{22}\oplus b_{22}\prec b_{11}\oplus b_{21}\oplus b_{21}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5148}%
$ b_1<b_2<b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5150}%
$ b_3<b_4<b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5152}%
$ \{b_1,b_2\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5154}%
$ \{b_3,b_4\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5156}%
$ b_1\oplus b_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5158}%
$ b_3\oplus b_4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5160}%
$ b_1\oplus b_2 ?  b_3\oplus b_4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5174}%
$ P_1\preccurlyeq_O P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5176}%
$\displaystyle \forall b_i\in O, \big(f_{P_1}(b_i)+\sum_{b_j\in O, b_i<b_j}f_{P_1}(b_j)\big)\leq\big(f_{P_2}(b_i)+\sum_{b_j\in O, b_i<b_j}f_{P_2}(b_j)\big)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5184}%
$ P_1\prec_O P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5186}%
$ (P_1\preccurlyeq_O
P_2)\wedge\neg(P_2\preccurlyeq P_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5194}%
$ P_1\succ_O P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5196}%
$ \neg(P_1\preccurlyeq_O
P_2)\wedge(P_2\preccurlyeq P_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5204}%
$ P_1=_O P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5206}%
$ (P_1\preccurlyeq_O P_2)\wedge(P_2\preccurlyeq
P_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5214}%
$ P_1?_O
P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5216}%
$ \neg(P_1\preccurlyeq_O P_2)\wedge\neg(P_2\preccurlyeq
P_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5218}%
$ P_1=b_{11}\oplus b_{13}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5220}%
$ P_2=b_{11}\oplus
b_{15}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5224}%
$ P_2\preccurlyeq_{O_1} P_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5225}%
$\displaystyle f_{P_2}(b_{11})=1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5226}%
$\displaystyle \leq 1=f_{P_1}(b_{11}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5227}%
$\displaystyle f_{P_2}(b_{11})\oplus f_{P_2}(b_{12})=1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5228}%
$\displaystyle \leq 1=f_{P_1}(b_{11})\oplus f_{P_1}(b_{12}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5229}%
$\displaystyle f_{P_2}(b_{11})\oplus f_{P_2}(b_{13})=1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5230}%
$\displaystyle \leq 2=f_{P_1}(b_{11})\oplus f_{P_1}(b_{13}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5231}%
$\displaystyle f_{P_2}(b_{11})\oplus f_{P_2}(b_{12})\oplus f_{P_2}(b_{14})=1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5232}%
$\displaystyle \leq 1=f_{P_1}(b_{11})\oplus f_{P_1}(b_{12})\oplus f_{P_1}(b_{14}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5233}%
$\displaystyle f_{P_2}(b_{11})\oplus f_{P_2}(b_{12})\oplus f_{P_2}(b_{13})\oplus f_{P_2}(b_{14})=2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5234}%
$\displaystyle \leq 2=f_{P_1}(b_{11})\oplus f_{P_1}(b_{12})\oplus f_{P_1}(b_{13})\oplus f_{P_1}(b_{14}).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5236}%
$ P_1\preccurlyeq_{O_1} P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5240}%
$ P_2\prec_{O_1} P_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5252}%
$\displaystyle \forall O_i\in\mathbf{O},(P_1\preccurlyeq_{O_i} P_2)\vee(\exists O_j\in\mathbf{O}, O_i\ll O_j\wedge P_1\prec_{O_j} P_2)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5264}%
$ \prec_O$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5266}%
$ \succ_O$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5268}%
$ =_O$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5270}%
$ ?_O$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5272}%
$ \preccurlyeq_O$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5274}%
$ P_1=b_{13}\oplus
b_{13}\oplus b_{21}\oplus b_{21}\oplus b_{21}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5276}%
$ P_2=b_{13}\oplus
b_{13}\oplus b_{21}\oplus b_{21}\oplus b_{22}\oplus b_{31}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5278}%
$ P_1=_{O_1}P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5280}%
$ P_1\succ_{O_2}P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5282}%
$ P_1\prec_{O_3}P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5294}%
$ O_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5296}%
$ O_3\gg O_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5302}%
$ P_1\preccurlyeq_{O_3}P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5307}%
$ Q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5309}%
$ n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5313}%
$ (n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5325}%
$ X_u(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5327}%
$ x\in X_u(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5333}%
$ x:d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5337}%
$ (n)\cup\{x:d\},\mathbf{C}\nvdash\bot$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5339}%
$ n'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5341}%
$ (n')=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5342}%
$ (n)\cup\{x:d\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5344}%
$ X_u(n')=X_u(n)-\{x\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5356}%
$\displaystyle \{x_i\mid$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5357}%
$\displaystyle (n), \mathbf{A}\vdash$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5358}%
$\displaystyle (x_i)\} -X_a(n)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5360}%
$ X_a(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{algorithm428}%
\begin{algorithm}
\begin{footnotesize}
 \begin{pseudocode}{solve}{\mathbf{X},\mathbf{D},\mathbf{C},\mathbf{A},P}
  n\GETS\text{new node};\\
  \text{solution}(n)\GETS\{\};\\
  X_u(n)\GETS\{x_i\mid\{\},\mathbf{A}\vdash\text{active}(x_i)\};\\
  X_a(n)\GETS\{\};\\
  CP(n)\GETS 0;\\
  PP(n)\GETS\oplus_{x\in \mathbf{X}}\max_{d\in D(x)} P(x:d);\\
  Q\GETS\text{createOrderedQueue}();\\
  \text{enqueue}(Q,n,PP(n),CP(n));
  \WHILE Q\neq\emptyset \DO
    \BEGIN
      n\GETS\text{dequeue}(Q);\\
      \IF X_u(n)\neq\emptyset
        \THEN  
          \BEGIN
            x\GETS\text{first}(X_u(n));\\
            \CALL{process}{x,n,\mathbf{C},\mathbf{A},P,Q};\\
          \END
        \ELSE
          \BEGIN     
            X_u(n)\GETS\{x_i\mid \text{solution}(n),\mathbf{A}\vdash\text{active}(x_i)\}-X_a(n);\\
            \IF X_u(n)=\emptyset
              \THEN 
                \BEGIN
                  n_{\text{next}}\GETS\text{first}(Q);\\
                  \IF CP(n)\nprec PP(n_{\text{first}})
                    \THEN \RETURN{\text{solution}(n)};
                    \ELSE
                      \BEGIN
                        PP(n)\GETS CP(n); \\
                        \text{enqueue}(Q,n,PP(n),CP(n));
                      \END\\
                \END
              \ELSE 
                \BEGIN
                  x\GETS\text{first}(X_u(n));\\
                  \CALL{process}{x,n,\mathbf{C},\mathbf{A},P,Q};\\
                \END
          \END
    \END\\
\PROCEDURE{process}{x,n_{\text{parent}},\mathbf{C},\mathbf{A},P,Q}
  \FOR d\in D(x) \DO
    \BEGIN
      \IF \text{solution}(n_{\text{parent}})\cup \{x:d\},\mathbf{C}\nvdash\bot
        \THEN
          \BEGIN
            n_{\text{child}}\GETS\text{new node};\\
            \text{solution}(n_{\text{child}})\GETS\text{solution}(n_{\text{parent}})\cup \{x:d\};\\
            X_d\GETS\text{deactivated}(\text{solution}(n_{\text{child}}),X(n_{\text{parent}}));\\
            X_{nd}(n_{\text{child}})\GETS X_{nd}(n_{\text{parent}})-\{x\}-X_d;\\
            X_a(n_{\text{child}})\GETS X_a(n_{\text{parent}})\cup\{x\};\\
            X_u(n_{\text{child}})\GETS X_u(n_{\text{parent}})-\{x\};\\
            CP(n_{\text{child}})\GETS CP(n_{\text{parent}})\oplus P(x:d);\\
            PP(n_{\text{child}})\GETS CP(n_{\text{child}})\oplus \oplus_{x\in X_{nd}(n)}\max_{d\in D(x)}P(x:d);\\
            \text{enqueue}(Q,n_{\text{child}},PP(n_{\text{child}}),CP(n_{\text{child}}));\\
          \END
    \END
\ENDPROCEDURE
\end{pseudocode}\end{footnotesize}
 \end{algorithm}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5366}%
$ CP(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5368}%
$ PP(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5371}%
$\displaystyle CP(n)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5372}%
$\displaystyle =\oplus_{x:d\in\text{solution}(n)}P(x:d)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5373}%
$\displaystyle PP(n)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5374}%
$\displaystyle =CP(n)\oplus(\oplus_{x\in X_{nd}(n)}\max_{d\in D_x}P(x:d))$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5376}%
$ X_{nd}(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5395}%
$ \CALL{solve}{\mathbf{X},\mathbf{D},\mathbf{C},\mathbf{A},P}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5399}%
$ PP(n)=CP(n)\oplus
h(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5405}%
$ h(n)=\oplus_{x\in X_{nd}(n)}\max_{d\in D_x}P(x:d)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5407}%
$ h(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5415}%
$ \delta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5417}%
$ \delta(P_1)\prec\delta(P_2)\leftrightarrow P_1\succ P_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5425}%
$ \delta(PP(n))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5427}%
$ \delta(PP(n))=\delta(CP(n))\oplus
\delta(h(n))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5429}%
$ \delta(h(n))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5435}%
$ S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5437}%
$ \delta(P(S))$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5439}%
$ P(S)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5441}%
\begin{displaymath}\begin{split} \mathbf{X}=\{&x_1,x_2,x_3,x_4,x_5,x_6\}\\D_{x_1}=\{&\text{yes},\text{no}\}\\D_{x_2}=\{&\text{yes},\text{no}\}\\D_{x_3}=\{&\text{yes},\text{no}\}\\D_{x_4}=\{&\text{other},\text{logistic}\}\\D_{x_5}=\{&\text{other},\text{logistic}\}\\D_{x_6}=\{&\text{Holling},\text{Lotka-Volterra}\}\\\end{split}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5443}%
$ x_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5445}%
$ x_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5447}%
$ x_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5449}%
$ x_4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5451}%
$ x_5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5453}%
$ x_6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5461}%
$ \mathbf{C}=\{c_{\{x_4,x_6\}},c_{\{x_5,x_6\}}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5463}%
\begin{displaymath}\begin{split} c_{\{x_4,x_6\}}=\{&\langle x_4:\text{other},x_6:\text{Lotka-Volterra}\rangle,\langle x_4:\text{logistic},x_6:\text{Holling}\rangle\}\\c_{\{x_5,x_6\}}=\{&\langle x_5:\text{other},x_6:\text{Lotka-Volterra}\rangle,\langle x_5:\text{logistic},x_6:\text{Holling}\rangle\} \end{split}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5465}%
$ \mathbf{A}=\{a_{x_4,\{x_1\}},a_{x_5,\{x_2\}},a_{x_6,\{x_1,x_2,x_3\}}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5467}%
\begin{displaymath}\begin{split} a_{x_4,\{x_1\}}=\{&\langle x_1:\text{yes},\text{active}(x_4)\rangle, \langle x_1:\text{no},\neg\text{active}(x_4)\rangle\}\\a_{x_5,\{x_2\}}=\{&\langle x_2:\text{yes},\text{active}(x_5)\rangle, \langle x_2:\text{no},\neg\text{active}(x_5)\rangle\}\\a_{x_6,\{x_1,x_2,x_3\}}=\{ &\langle x_1:\text{yes},x_2:\text{yes},x_3:\text{yes},\text{active}(x_4)\rangle,\langle x_1:\text{yes},x_2:\text{yes},x_3:\text{no},\neg\text{active}(x_4)\rangle,\\&\langle x_1:\text{yes},x_2:\text{no},x_3:\text{yes},\neg\text{active}(x_4)\rangle,\langle x_1:\text{yes},x_2:\text{no},x_3:\text{no},\neg\text{active}(x_4)\rangle,\\&\langle x_1:\text{no},x_2:\text{yes},x_3:\text{yes},\neg\text{active}(x_4)\rangle,\langle x_1:\text{no},x_2:\text{yes},x_3:\text{no},\neg\text{active}(x_4)\rangle,\\&\langle x_1:\text{no},x_2:\text{no},x_3:\text{yes},\neg\text{active}(x_4)\rangle,\langle x_1:\text{no},x_2:\text{no},x_3:\text{no},\neg\text{active}(x_4)\rangle\} \end{split}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5469}%
$ O_{\text{growth}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5471}%
$ O_{\text{predation}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5473}%
$ O_{\text{growth}}\ll O_{\text{predation}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5475}%
\begin{displaymath}\begin{split} O_{\text{growth}}=   &\{p_{\text{other}},p_{\text{logistic}}\}\text{ with }p_{\text{logistic}}<p_{\text{other}}\\O_{\text{predation}}=&\{p_{\text{Holling}},p_{\text{Lotka-Volterra}}\}\text{   with }p_{\text{Lotka-Volterra}}<p_{\text{Holling}} \end{split}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5477}%
\begin{displaymath}\begin{split} P(x_4:\text{other})=P(x_5:\text{other})=&p_{\text{other}}\\P(x_4:\text{logistic})=P(x_5:\text{logistic})=&p_{\text{logistic}}\\P(x_6:\text{Holling})=&p_{\text{Holling}}\\P(x_6:\text{Lotka-Volterra})=&p_{\text{Lotka-Volterra}} \end{split}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5479}%
$ n_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5481}%
$ X_u(n_0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5483}%
$ \{x_1,x_2,x_3\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5485}%
$ X_a(n_0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5487}%
$ CP(n_0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5489}%
$ PP(n_0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5491}%
$ p_{\text{other}}\oplus
p_{\text{other}}\oplus p_{\text{Holling}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5495}%
$ PP$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5497}%
$ CP$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5501}%
$ i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5503}%
$ n_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure671}%
\begin{figure}\centering\epsfig{file=../../../figures/ecomod-aDPCSP-trace.eps,height=15cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5508}%
$ n_5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5510}%
$ X_u(n_5)=\{\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5516}%
$ \{x_1:$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5517}%
$ ,x_2:$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5518}%
$ ,x_3:$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5519}%
$ \}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5521}%
$ X_u(n_5)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5523}%
$ \{x_4,x_5,x_6\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5525}%
$ n_{12}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5527}%
$\displaystyle \{x_1:$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5528}%
$\displaystyle ,x_2:$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5529}%
$\displaystyle ,x_3:$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5530}%
$\displaystyle ,x_4:$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5531}%
$\displaystyle ,x_5:$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5532}%
$\displaystyle ,x_6:$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5533}%
$\displaystyle \}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5539}%
$ n_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5541}%
$ n_4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5543}%
$ PP(n_2)=PP(n_4)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5545}%
$ CP(n_2)=CP(n_4)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5547}%
$\displaystyle \{n_{10},n_8,n_{12},n_6,n_2,n_4\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5549}%
$ n_9$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5553}%
$ n_{10}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5555}%
$ n_{19}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5559}%
$\displaystyle \{n_{19},n_{12},n_6,n_2,n_4\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5565}%
$ X_u(n_{19})=\emptyset$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5573}%
$ PP(n_{12})\prec CP(n_{19})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5577}%
$ n_i\wedge\ldots\wedge n_j\wedge\neg n_k\wedge\ldots\wedge\neg
n_l\rightarrow n_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5579}%
$ n_i,\ldots,n_j,n_k,\ldots,n_l,n_m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5581}%
$ n_i\wedge\ldots\wedge n_j\wedge\neg
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5583}%
$ \{n_i,\ldots,n_j,\neg n_k,\ldots,\neg n_l\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5585}%
$ E$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5589}%
$ {\cal L}(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5595}%
$\displaystyle \forall E\in{\cal L}(n),[(\wedge_{n_i\in E}n_i) \wedge(\wedge_{\neg n_i\in E}\neg n_i)]\vdash n$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5597}%
$\displaystyle \forall E\in{\cal L}(n),[(\wedge_{n_i\in E}n_i)\wedge (\wedge_{\neg n_i\in E}\neg n_i)]\nvdash\bot$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5599}%
$\displaystyle \forall E\in{\cal L}(n)\nexists E'\in{\cal L}(n), E'\subset E$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5601}%
\begin{displaymath}\begin{split}       \forall E,&[(\wedge_{n_i\in E}n_i) \wedge (\wedge_{\neg n_i\in E}\neg n_i)\vdash n]\\&\exists E'\in{\cal L}(n),[(\wedge_{n_i\in E'}n_i) \wedge     (\wedge_{\neg n_i\in E'}\neg n_i) \vdash n]     \end{split}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5608}%
$\displaystyle \frac{d}{dt}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5609}%
$\displaystyle =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5610}%
$\displaystyle \times$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5611}%
$\displaystyle \times(1-\frac{\text{size}}{\text{capacity}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5612}%
$\displaystyle \texttt{(predation frog insect)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5613}%
$\displaystyle \texttt{(d/dt change (* change-rate size (- 1 (/ size capacity))))}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5615}%
$ \langle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5617}%
$ \rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5618}%
$\displaystyle \texttt{(relevant}\quad\langle\textit{name}\rangle\quad[\{\langle\textit{participant}\rangle\}\mid\langle\textit{relation}\rangle]\texttt{)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5619}%
$\displaystyle \texttt{(relevant growth ?population)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5624}%
$\displaystyle \texttt{(model}\quad[\langle\textit{participant}\rangle\mid\langle\textit{relation}\rangle]\quad\langle\textit{name}\rangle\texttt{)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5625}%
$\displaystyle \texttt{(model ?population logistic)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5628}%
$ \langle
P,R\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5632}%
$ R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath5638}%
\begin{displaymath}\begin{split} P&=\{\texttt{predator},\texttt{prey}\}\\R&=\{\texttt{(predation predator prey)}\} \end{split}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure840}%
\begin{figure}\centering\epsfig{file=../../../figures/holling1.eps, width=90mm}\end{figure}%
\lthtmlfigureZ
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{\newpage\clearpage
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$ N_{\text{predator}}$%
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{\newpage\clearpage
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$ N_{\text{prey}}$%
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$ B_{\text{predator}}$%
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{\newpage\clearpage
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$ B_{\text{prey}}$%
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{\newpage\clearpage
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$ D_{\text{predator}}$%
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{\newpage\clearpage
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$ D_{\text{prey}}$%
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{\newpage\clearpage
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$ P_{\text{prey}}$%
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{\newpage\clearpage
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$ b_{\text{predator}}$%
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{\newpage\clearpage
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$ b_{\text{prey}}$%
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{\newpage\clearpage
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$ d_{\text{predator}}$%
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{\newpage\clearpage
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$ d_{\text{prey}}$%
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{\newpage\clearpage
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$ C_{\text{predator}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5667}%
$ C_{\text{prey}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5669}%
$ s_{\text{(prey,predator)}}$%
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{\newpage\clearpage
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$ t_{\text{(prey,predator)}}$%
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{\newpage\clearpage
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$ r_{\text{(predator,prey)}}$%
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\lthtmldisplayA{displaymath5702}%
\begin{displaymath}\begin{split} P=\{ &N_{\text{predator}},B_{\text{predator}},D_{\text{predator}},N_{\text{prey}},B_{\text{prey}},D_{\text{prey}},P_{\text{prey}},\\&b_{\text{predator}},b_{\text{prey}},d_{\text{predator}},d_{\text{prey}},C_{\text{predator}},C_{\text{prey}},\\&s_{(\text{prey},\text{predator})},t_{(\text{prey},\text{predator})},r_{(\text{predator},\text{prey})}\} \end{split}\end{displaymath}%
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\begin{displaymath}\begin{split} R=\{ &\frac{d}{dt}N_{\text{predator}}=B_{\text{predator}}-D_{\text{predator}},\\&\frac{d}{dt}N_{\text{prey}}=B_{\text{prey}}-D_{\text{prey}}-P_{\text{prey}},\\&B_{\text{predator}}=b_{\text{predator}}\times N_{\text{predator}},\\&B_{\text{prey}}=b_{\text{prey}}\times N_{\text{prey}},\\&D_{\text{predator}}=d_{\text{predator}}\times N_{\text{predator}}\times\frac{N_{\text{predator}}}{C_{\text{predator}}},\\&D_{\text{prey}}=d_{\text{prey}}\times N_{\text{prey}}\times\frac{N_{\text{prey}}}{C_{\text{prey}}},\\&P_{\text{prey}}=\frac{s_{(\text{prey},\text{predator})}\times N_{\text{prey}}\times N_{\text{predator}}}                      {1+ s_{(\text{prey},\text{predator})}\times N_{\text{prey}}\times t_{(\text{prey},\text{predator})}},\\&C_{\text{predator}}=r_{(\text{predator},\text{prey})}\times N_{\text{prey}},\\&C_{\text{prey}}=N_{\text{prey}} \} \end{split}\end{displaymath}%
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$\displaystyle \frac{d}{dt}N_{\text{prey}}=B_{\text{prey}}-D_{\text{prey}}-P_{\text{prey}}$%
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{\newpage\clearpage
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$ B_{\text{prey}}-D_{\text{prey}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5724}%
$\displaystyle \frac{d}{dt}N_{\text{prey}}=C^+(B_{\text{prey}})\qquad  \frac{d}{dt}N_{\text{prey}}=C^-(D_{\text{prey}})\qquad \frac{d}{dt}N_{\text{prey}}=C^-(P_{\text{prey}})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5726}%
$ = C^+($%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5727}%
$ )$%
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{\newpage\clearpage
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$ = C^-($%
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{\newpage\clearpage
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$ = C^{\times}($%
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{\newpage\clearpage
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$ = C^{\div}($%
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$ =C^{\text{if},p}(\text{antecedent}, \text{formula})$%
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{\newpage\clearpage
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$ =C^{\text{else}}(\text{formula})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5765}%
$ f$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5767}%
$ v=C^+(f)$%
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{\newpage\clearpage
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$ v=C^-(f)$%
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{\newpage\clearpage
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$ -f$%
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{\newpage\clearpage
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$ v=C^{\times}(f)$%
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{\newpage\clearpage
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$ v=C^{\div}(f)$%
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{\newpage\clearpage
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$ \frac{1}{f}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5785}%
$\displaystyle c_1$%
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{\newpage\clearpage
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$\displaystyle v=r_1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5787}%
$\displaystyle c_2\ldots$%
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{\newpage\clearpage
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$\displaystyle v=r_n$%
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{\newpage\clearpage
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$ v$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5792}%
$ c_i$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5794}%
$ i=1,\ldots,n-1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5796}%
$ r_j$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5798}%
$ j=1,\ldots,n$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath5800}%
\begin{displaymath}\begin{split} &\text{if }c_i\text{ then }v=r_i\qquad\text{ with }i=1,\ldots,n-1\\&\text{else }v=r_n \end{split}\end{displaymath}%
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{\newpage\clearpage
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$ v=C^{\text{if},p}(a,f)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5810}%
$ a$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5814}%
$ v=C^{\text{else}}(f_{\text{else}})$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5816}%
$ f_{\text{else}}$%
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{\newpage\clearpage
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\begin{displaymath}\begin{split} v&=C^{\text{if},p_1}(c_1,r_1)\\&\vdots\\v&=C^{\text{if},p_{n-1}}(c_{n-1},r_{n-1})\\v&=C^{\text{else}}(r_n) \end{split}\end{displaymath}%
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{\newpage\clearpage
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$ p_1>\ldots>p_{n-1}$%
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{\newpage\clearpage
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$ C^+(f_2)$%
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{\newpage\clearpage
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$ C^-(f_2)$%
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{\newpage\clearpage
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$ C^{\times}(f_2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5830}%
$ C^{\div}(f_2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5832}%
$ C^{\text{if},p_2}(a_2,f_2)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5834}%
$ C^{\text{else}}(f_2)$%
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{\newpage\clearpage
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$ C^+(f_1)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5838}%
$ C^-(f_1)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5840}%
$ C^{\times}(f_1)$%
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{\newpage\clearpage
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$ C^{\div}(f_1)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5844}%
$ C^{\text{if},p_1}(a_1,f_1)$%
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{\newpage\clearpage
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$ C^{\text{if},p_2}(a_1,f_1)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5848}%
$ C^{\text{else}}(f_1)$%
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{\newpage\clearpage
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$ x=C^+(y)$%
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{\newpage\clearpage
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$ x=C^-(z)$%
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{\newpage\clearpage
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$ x=y-z$%
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{\newpage\clearpage
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$ x=C^{\times}(z)$%
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{\newpage\clearpage
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$ x=y+z$%
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{\newpage\clearpage
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$ x=y\times z$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5923}%
$ C^{\text{else}}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5926}%
$\displaystyle R(v,C^+)=\{v=C^+(f_i)\mid (v=C^+(f_i))\in R\}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5927}%
$\displaystyle R(v,C^-)=\{v=C^-(f_i)\mid (v=C^-(f_i))\in R\}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5928}%
$\displaystyle R(v,C^{\times})=\{v=C^{\times}(f_i)\mid (v=C^{\times}(f_i))\in R\}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5929}%
$\displaystyle R(v,C^{\div})=\{v=C^{\div}(f_i)\mid (v=C^{\div}(f_i))\in R\}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5930}%
$\displaystyle R(v,C^{\text{if}})=\{v=C^{\text{if},p_i}(a_i,f_i)\mid (v=C^{\text{if},p_i}(a_i,f_i))\in R\}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5931}%
$\displaystyle R(v,C^{\text{else}})=\{v=C^{\text{else}}(f_i)\mid (v=C^{\text{else}}(f_i))\in R\}$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath5937}%
\begin{displaymath}\begin{split} R(v,C^+)=\{v=C^+(f_{1+}),\ldots,v=C^+(f_{m+})\}&\wedge\\R(v,C^-)=\{v=C^-(f_{1-}),\ldots,v=C^-(f_{n-})\}&\rightarrow\\v=f_{1+}+\ldots+f_{m+}-(f_{1-}+\ldots+f_{n-})& \end{split}\end{displaymath}%
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{\newpage\clearpage
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\begin{displaymath}\begin{split} R(v,C^{\times})=\{v=C^{\times}(f_{1{\times}}),\ldots,v=C^{\times}(f_{m{\times}})\}&\wedge\\R(v,C^{\div})=\{v=C^{\div}(f_{1{\div}}),\ldots,v=C^{\div}(f_{n{\div}})\}&\rightarrow\\v=\frac{1\times f_{1{\times}}\times\ldots\times f_{m{\times}}}{f_{1{\div}}\times\ldots\times f_{n{\div}}}& \end{split}\end{displaymath}%
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{\newpage\clearpage
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\begin{displaymath}\begin{split} R(v,C^{\text{if}})=&\{v=C^{\text{if},p_1}(a_1,f_1),\ldots,v=C^{\text{if},p_m}(a_m,f_m)\}\wedge\\R(v,C^{\text{else}})=&\{v=C^{\text{else}}(f_{\text{else}})\}\wedge p_1>\ldots> p_m \rightarrow\\v=&\text{if }a_1\text{ then }f_1,\text{ else }\ldots,\text{if }a_m\text{ then }f_m,\text{else }f_{\text{else}} \end{split}\end{displaymath}%
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$ \Pi$%
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{\newpage\clearpage
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$ \langle P^s,\Phi,\pi\rangle$%
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{\newpage\clearpage
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$ P^s=\{p_1^s,\ldots
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{\newpage\clearpage
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$ \Phi$%
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{\newpage\clearpage
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$ P^s$%
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{\newpage\clearpage
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$ \pi$%
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{\newpage\clearpage
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$\displaystyle \forall p_1^s,\ldots,\forall p_m^s\Phi\rightarrow\pi$%
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{\newpage\clearpage
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$ \texttt{?v}=\texttt{*}$%
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{\newpage\clearpage
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$ \frac{d}{dt}\texttt{?v}=\texttt{*}$%
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$ \mu$%
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{\newpage\clearpage
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$ \langle
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{\newpage\clearpage
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{\newpage\clearpage
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$ \Phi^s=\{\phi_1^s,\ldots,\phi_v^s\}$%
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{\newpage\clearpage
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$ \Phi^t=\{\phi_1^t,\ldots,\phi_x^t\}$%
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{\newpage\clearpage
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$ P^s\cup P^t$%
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{\newpage\clearpage
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$ A=\{a_1,\ldots,a_y\}$%
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{\newpage\clearpage
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$ \Pi=$%
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{\newpage\clearpage
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$\displaystyle \forall \phi_i^t\in\Phi^t,\forall p_1^s,\ldots,\forall p_m^s,\exists p_1^t,\ldots,\exists p_n^t,\thickspace\phi_1^s\wedge\ldots\wedge\phi_v^s \rightarrow(a_1\wedge\ldots\wedge a_y\rightarrow\phi_i^t)$%
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{\newpage\clearpage
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$\displaystyle \forall \pi\in\Pi, \forall p_1^s,\ldots,\forall p_m^s,\forall p_1^t,\ldots,\forall p_n^t,\thickspace\phi_1^s\wedge\ldots\wedge\phi_v^s\wedge a_1\wedge\ldots\wedge a_x\wedge\neg\pi\rightarrow\bot$%
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{\newpage\clearpage
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$ \langle
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{\newpage\clearpage
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$\displaystyle \frac{d}{dt}\texttt{?p-size}=\texttt{?p-change}$%
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$ \Pi=\langle \Pi_S,P\rangle$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6000}%
$ \Pi_S$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figurestar1267}%
\begin{figure*}\centering\epsfig{file=../../../figures/cem-architecture-jair.eps,width=13cm}\end{figure*}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6009}%
$ \CALL{generateModelSpace}{\langle O,R\rangle}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6011}%
$ \langle O,R\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6013}%
$ \theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6029}%
$ (\mu,\theta,\sigma)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6033}%
$ \sigma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6037}%
$\displaystyle (\mu,\theta,\sigma)= \begin{cases} \text{true}     & \text{if } \quad\sigma=\{p^s_1/o_1,\ldots,p^s_m/o_m\}\wedge\\& \qquad P^s(\mu)=\{p^s_1,\ldots,p^s_m\}\wedge\\& \qquad o_1\in\theta\wedge\ldots\wedge o_m\in\theta\wedge\\& \qquad \forall \phi\in\Phi^s(\mu), \sigma\phi\in\theta\\\text{false}    & \text{otherwise} \end{cases}$%
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{\newpage\clearpage
\lthtmlfigureA{algorithm1297}%
\begin{algorithm}
\begin{footnotesize}
 \begin{pseudocode}{generateModelSpace}{\langle O,R\rangle}
  \theta\GETS\text{new ATMS};\\
  \FOREACH o\in O, \text{add-node}(\theta,o);\\
  \FOREACH r\in R, \text{add-node}(\theta,r);\\
  \FOREACH \mu,\sigma, \text{match}(\mu,\theta,\sigma) \DO
    \BEGIN
      \text{justification}\GETS\emptyset;\\
      \FOREACH a\in A(\mu) \DO
        \BEGIN
          \text{newnode}\GETS\text{add-node}(\theta,(\sigma a));\\
          \text{justification}\GETS\text{justification}\cup\{\text{newnode}\};\\
        \END\\
      \FOREACH p\in P^s(\mu)
        \DO \text{justification}\GETS\text{justification}\cup\{\text{find-node}(\theta,(\sigma p))\};\\
      \FOREACH \phi\in \Phi^s(\mu)
        \DO \text{justification}\GETS\text{justification}\cup\{\text{find-node}(\theta,(\sigma \phi))\};\\
      \text{add-node}(\theta,n_{(\sigma,\mu)});\\
      \text{add-justification}(\theta,n_{(\sigma,\mu)},\wedge_{n\in\text{justification}}n);\\
      \FOREACH p\in P^t(\mu) \DO
        \BEGIN
          \sigma\GETS\sigma\cup\{p/\text{gensym}()\};\\
          o\GETS\text{add-node}(\theta,(\sigma p));\\
          \text{add-justification}(\theta,o,n_{(\sigma,\mu)});\\
        \END\\
      \FOREACH \phi\in \Phi^t(\mu) \DO
        \BEGIN
          \IF (\sigma \phi\in\theta) 
            \THEN o\GETS\text{get-node}(\theta,(\sigma \phi));
            \ELSE o\GETS\text{add-node}(\theta,(\sigma \phi));\\
          \text{add-justification}(\theta,o,n_{(\sigma,\mu)});\\
        \END
    \END\\
  \FOREACH n_1,\ldots,n_m, \text{inconsistent}(\{n_1,\ldots,n_m)
    \DO \text{add-justification}(\theta,n_\bot,n_1\wedge\ldots\wedge n_m);
\end{pseudocode}\end{footnotesize}
 \end{algorithm}%
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{\newpage\clearpage
\lthtmlfigureA{figurestar1336}%
\begin{figure*}\centering\epsfig{file=../../../figures/model-space-theory.eps,width=14cm}\end{figure*}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6046}%
$ a\in A(\mu)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6048}%
$ \sigma a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6052}%
$ n_{(\sigma,\mu)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6060}%
$\displaystyle (\wedge_{a\in A(\mu)}\sigma a)\wedge(\wedge_{p\in P^s(\mu)}\sigma     p)\wedge(\wedge_{\phi\in \Phi^s(\mu)}\sigma \phi)\rightarrow     n_{(\sigma,\mu)}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6062}%
$ p\in
P^t(\mu)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6064}%
$ \phi\in\Phi^t(\mu)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6066}%
$ \sigma\phi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6070}%
$ ()$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6074}%
$ \{p/$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6075}%
$ ()\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6081}%
$ \sigma p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6085}%
$ n_{(\sigma,\mu)}\rightarrow n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6087}%
$ \mu=\langle
P^s,P^t,\Phi^s,\Phi^t,A,\{\}\rangle$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1354}%
\begin{figure}\centering\mbox{
\subfigure[Inconsistency caused by a global property]{
  \epsfig{file=../../../figures/cem-inconsistencies-1.eps,height=37mm}}
\quad
\subfigure[Inconsistency caused by a purpose-required property]{
  \epsfig{file=../../../figures/cem-inconsistencies-2.eps,height=37mm}}\quad
\subfigure[Inconsistency caused by non-composable relations]{
  \epsfig{file=../../../figures/cem-inconsistencies-3.eps,height=37mm}}
}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6094}%
$ \{n_1,\ldots,n_m\}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6096}%
$ (\{n_1,\ldots,n_m\})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6102}%
$ (\{\neg\pi\})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6108}%
$ \Pi(\mu)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6116}%
$ n_{\sigma\pi}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6118}%
$ \pi\in\Pi(\mu)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6120}%
$ (\{n_{(\sigma,\mu)},\neg n_{\sigma\pi}\})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6122}%
$ v=r_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6124}%
$ v=r_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6126}%
$ r_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6129}%
$\displaystyle x=C^+(y)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6130}%
$\displaystyle x=C^{\times}(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6132}%
$ C^+$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6134}%
$ C^{\times}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6135}%
$\displaystyle a=C^+(b)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6136}%
$\displaystyle a=c+d$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6138}%
$ c+d$%
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{\newpage\clearpage
\lthtmlfigureA{figure1387}%
\begin{figure}\centering\epsfig{file=../../../figures/popgrowth.eps,width=10cm}\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6144}%
$ \CALL{createaDCSP}{\mbox{}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{algorithm1400}%
\begin{algorithm}
\begin{footnotesize}
 \begin{pseudocode}{createaDCSP}{\mbox{}}
\COMMENT{$\sigma$\  is the set of substitutions}\\
\sigma\GETS\{\};\\
\COMMENT{Generate attributes and domains}\\
\FOREACH A,\text{assumption-class}(A) \DO
  \BEGIN
    x\GETS\text{create-attribute}();\\
    D(x)\GETS\{\};\\
    \sigma\GETS\sigma\cup\{A/x\};\\
    \FOREACH a\in A \DO
      \BEGIN
        v\GETS\text{create-value}();\\
        D(x)\GETS D(x)\cup\{v\};\\
        \sigma\GETS\sigma\cup\{a/x:v\};\\
      \END
  \END\\
\COMMENT{Generate activity constraints}\\
\FOREACH A,\text{assumption-class}(A) \DO
  \BEGIN
    s\GETS\text{subject}(A);\\
    \FOREACH \{a_{1\top},\ldots,a_{p\top},\neg a_{1\bot},\ldots,\neg
    a_{q\bot}\}\in{\cal L}(s) \DO
      \text{add}(\sigma a_{1\top}\wedge\ldots\wedge\sigma
      a_{p\top}\wedge\sigma \neg
      a_{1\bot}\wedge\ldots\wedge\sigma\neg
      a_{q\bot}\rightarrow\text{active}(\sigma A));\\
  \END\\
\COMMENT{Generate compatibility constraints}\\
\FOREACH \{a_{1\top},\ldots,a_{p\top},\neg a_{1\bot},\ldots,\neg a_{q\bot}\}\in{\cal L}(n_{\bot}) \DO
  \text{add}(\sigma a_{1\top}\wedge\ldots\wedge\sigma a_{p\top}\wedge\sigma \neg a_{1\bot}\wedge\ldots\wedge\sigma\neg a_{q\bot}\rightarrow\bot);
\end{pseudocode}\end{footnotesize}
 \end{algorithm}%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6146}%
$ A_1=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6148}%
$ \neg$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6150}%
$ A_2=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6152}%
$ \texttt{n}_{\text{frog}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6166}%
$ A_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6168}%
$ {\cal
L}(\bot)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6193}%
$ s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6195}%
$ \frac{d}{dt}s=C^+(f)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6201}%
$ \frac{d}{dt}s=C^-(f)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6203}%
$\displaystyle \frac{d}{dt}\texttt{?stock}=C^+(\texttt{?flow})$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6205}%
$\displaystyle \frac{d}{dt}\texttt{?stock}=C^-(\texttt{?flow})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6207}%
$\displaystyle \frac{d}{dt}\texttt{?stock1}=C^-(\texttt{?flow})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay6208}%
$\displaystyle \frac{d}{dt}\texttt{?stock2}=C^+(\texttt{?flow})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1565}%
\begin{figure}\centering\mbox {\subfigure[Exponential growth]{\epsfig{file=../../../figures/exponential-1-math.eps,width=.45\textwidth}}
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       \subfigure[Logistic growth]{\epsfig{file=../../../figures/logistic-1-math.eps,width=.45\textwidth}}
}
\end{figure}%
\lthtmlfigureZ
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{\newpage\clearpage
\lthtmlfigureA{figure1609}%
\begin{figure}\centering\mbox {\subfigure[Lotka-Volterra predation]{\epsfig{file=../../../figures/lotka-volterra-11-math.eps,width=.45\textwidth}}
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       \subfigure[Holling predation]{\epsfig{file=../../../figures/holling-11-math.eps,width=.45\textwidth}}
}
\end{figure}%
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{\newpage\clearpage
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\begin{figure}\centering\epsfig{file=../../../figures/competition-11-math.eps,width=8cm}\end{figure}%
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmldisplayA{displaymath6225}%
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\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6228}%
$ x_{1}$%
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{\newpage\clearpage
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$ x_{2}$%
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{\newpage\clearpage
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$ x_{3}$%
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{\newpage\clearpage
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$ x_{4}$%
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{\newpage\clearpage
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$ x_{5}$%
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{\newpage\clearpage
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$ x_{6}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6240}%
$ x_{7}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6242}%
$ x_{8}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6244}%
$ x_{9}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6246}%
$ x_{10}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6248}%
$ x_{11}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6277}%
$ D_{1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6279}%
$ \{d_{1,y},d_{1,n}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6281}%
$ D_{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6283}%
$ \{d_{2,y},d_{2,n}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6285}%
$ D_{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6287}%
$ \{d_{3,y},d_{3,n}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6289}%
$ D_{4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6291}%
$ \{d_{4,y},d_{4,n}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6293}%
$ D_{5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6295}%
$ \{d_{5,y},d_{5,n}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6297}%
$ D_{6}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6299}%
$ \{d_{6,y},d_{6,n}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6301}%
$ D_{7}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6303}%
$ \{d_{7,l},d_{7,e},d_{7,o}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6305}%
$ D_{8}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6307}%
$ \{d_{8,l},d_{8,e},d_{8,o}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6309}%
$ D_{9}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6311}%
$ \{d_{9,l},d_{9,e},d_{9,o}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6313}%
$ D_{10}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6315}%
$ \{d_{10,h},d_{10,lv}\}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$ D_{11}$%
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\stepcounter{section}

\end{document}
