State complexity of permutation on finite languages over a binary alphabet

초록

The set of all strings Parikh equivalent to a string in a language L is called the permutation of L. The permutation of a finite n-state DFA (deterministic finite automaton) language over a binary alphabet can be recognized by a DFA with n(2)-n+2/2 states. We show that if the language consists of equal length binary strings the bound can be improved to f(n) = n(2)-n+1/3 and for every n congruent to I modulo 3 there exists an n-state DFA A recognizing a set of equal length strings such that the minimal DFA for the permutation of L(A) needs f (n) states. (C) 2017 Elsevier B.V. All rights reserved.

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