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expressing_finite_automata_in_msol_over_strings [2010/05/21 02:31] vkuncak |
expressing_finite_automata_in_msol_over_strings [2012/05/15 12:43] vkuncak |
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| - | ====== Expressing finite automaton in MSOL over strings ====== | + | ====== Expressing finite automaton in WS1S ====== |
| Consider a finite automaton with alphabet $\Sigma=\{0,1\}^n$, states $Q = \{q_0,q_1,\ldots,q_m\}$, transition relation $\Delta$, initial state $q_0$ and final states $F$. | Consider a finite automaton with alphabet $\Sigma=\{0,1\}^n$, states $Q = \{q_0,q_1,\ldots,q_m\}$, transition relation $\Delta$, initial state $q_0$ and final states $F$. | ||
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| Then the word is accepted if the above formula holds for the entire input | Then the word is accepted if the above formula holds for the entire input | ||
| \[ | \[ | ||
| - | \exists k. (F \land \forall p. k < p \rightarrow \bidwedge_i p \notin v_i) | + | \exists k. (F \land \forall p. k < p \rightarrow \bigwedge_i p \notin v_i) |
| \] | \] | ||