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msol_over_strings [2007/05/08 20:32] vaibhav.rajan |
msol_over_strings [2007/05/10 18:14] vkuncak |
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====== MSOL over Strings ====== | ====== MSOL over Strings ====== | ||
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===== Syntax and Semantics of Weak Monadic Second-Order Logic over Strings ===== | ===== Syntax and Semantics of Weak Monadic Second-Order Logic over Strings ===== | ||
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[\![v_1 \subseteq v_2]\!]e &=& (e(v_1) \subseteq e(v_2)) \\ \ | [\![v_1 \subseteq v_2]\!]e &=& (e(v_1) \subseteq e(v_2)) \\ \ | ||
[\![s(v_1,v_2)]\!]e &=& (\exists k \in N_0. e(v_1) = \{k\} \land e(v_2)=\{k+1\}) \\ \ | [\![s(v_1,v_2)]\!]e &=& (\exists k \in N_0. e(v_1) = \{k\} \land e(v_2)=\{k+1\}) \\ \ | ||
- | [\![F_1 \lor F_2]\!]e &=& [\![F_1]\!]e\ \land\ [\![F_2]\!]e \\ \ | + | [\![F_1 \lor F_2]\!]e &=& [\![F_1]\!]e\ \lor\ [\![F_2]\!]e \\ \ |
[\![\lnot F]\!]e &=& \lnot ([\![F]\!]e) \\ \ | [\![\lnot F]\!]e &=& \lnot ([\![F]\!]e) \\ \ | ||
- | [\![\exists v. F]\!] &=& \exists S \subseteq N_0. [\![F]\!](e[v \mapsto S]) | + | [\![\exists v. F]\!]e &=& \exists S. S \mbox{is finite}\ \land\ S \subseteq N_0. [\![F]\!](e[v \mapsto S]) |
\end{eqnarray*} | \end{eqnarray*} | ||