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msol_over_strings [2007/05/06 19:03] vkuncak created |
msol_over_strings [2007/05/08 20:32] vaibhav.rajan |
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| + | ====== MSOL over Strings ====== | ||
| ===== 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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| **Set operations**. The ideas is that quantification over sets with $\subseteq$ gives us the full Boolean algebra of sets. | **Set operations**. The ideas is that quantification over sets with $\subseteq$ gives us the full Boolean algebra of sets. | ||
| - | * Two sets are equal: $(S_1 = S_2) = (S_1 \subeteq S_2) \land (S_2 \subseteq S_1)$ | + | * Two sets are equal: $(S_1 = S_2) = (S_1 \subseteq S_2) \land (S_2 \subseteq S_1)$ |
| * Strict subset: $(S_1 \subset S_2) = (S_1 \subseteq S_2) \land \lnot (S_2 \subseteq S_1)$ | * Strict subset: $(S_1 \subset S_2) = (S_1 \subseteq S_2) \land \lnot (S_2 \subseteq S_1)$ | ||
| * Set is empty: $(S=\emptyset) = \forall S_1. S \subseteq S_1$ | * Set is empty: $(S=\emptyset) = \forall S_1. S \subseteq S_1$ | ||