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--- expressing_finite_automata_in_msol_over_strings [2009/04/29 11:09]
vkuncak
+++ expressing_finite_automata_in_msol_over_strings [2010/05/21 02:31]
vkuncak
@@ Line 18: / Line 18: @@
 \end{equation*}
-To express the property that an automaton accepts a string whose length is given by free variable $k$ we then use formula
+To express the property that an automaton accepts a string whose length is given by free variable $k$ we then use formula $F$:
 \begin{equation*}
   \exists Q_0,\ldots, Q_m.\ \mbox{Init} \land (\forall p. p \leq k \rightarrow \mbox{Trans}) \land \mbox{Final}
 \end{equation*}
+Then the word is accepted if the above formula holds for the entire input
+\[
+   \exists k. (F \land \forall p. k < p \rightarrow \bigwedge_i p \notin v_i)
+\]