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expressing_regular_expressions_in_msol_over_strings [2007/05/06 20:59] vkuncak created |
expressing_regular_expressions_in_msol_over_strings [2007/05/06 21:01] vkuncak |
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====== Expressing regular expressions in MSOL over strings ====== | ====== Expressing regular expressions in MSOL over strings ====== | ||

- | Idea: for each regular expression $r$ of alphabet with inputs $v_1,\ldots,v_n$ associate a formula $F$ with free variables $v_1,\ldots,v_n,p,q$ such that $F$ is valid precisely for whose sets of numbers for which | + | Idea: for each regular expression $r$ of a [[regular expressions for automata with parallel inputs|automaton for parallel inputs]] $v_1,\ldots,v_n$ associate a formula $F$ with free variables $v_1,\ldots,v_n,p,q$ such that $F$ is valid precisely for whose sets of numbers for which |

* $p$ and $q$ are singletons | * $p$ and $q$ are singletons | ||

* the strings given by the parts of $v_1,\ldots,v_n$ that start at position $p$ and end at position $q$ satisfy regular expression $F(r)$ | * the strings given by the parts of $v_1,\ldots,v_n$ that start at position $p$ and end at position $q$ satisfy regular expression $F(r)$ |