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Efficient Equivalence and Minimization for Non Deterministic Xor Automata

Jean Vuillemin 1, * Nicolas Gama 2 
* Corresponding author
2 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
Abstract : A word w in a regular language L is or-accepted by a non-deterministic finite or-automaton A if there exists a path along w from some initial state to some final state in A. The same word w is xor-accepted by the same non-deterministic finite xor-automaton A if the number of accepting pathes is odd. In the deterministic case, accepting pathes are unique and both definitions coincide. No polynomial time algorithm is known to minimize NFAs or to compute their equivalence. By contrast, we present a cubic time algorithm to reduce a xor-automaton to a minimal form M = MXA(A), within the least possible number of states. It is a finite strong normal form and automata equivalence is efficiently decided through reduction to the SNF.
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Submitted on : Thursday, May 27, 2010 - 4:57:20 PM
Last modification on : Wednesday, October 26, 2022 - 8:16:43 AM
Long-term archiving on: : Thursday, September 16, 2010 - 3:27:51 PM


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  • HAL Id : inria-00487031, version 1


Jean Vuillemin, Nicolas Gama. Efficient Equivalence and Minimization for Non Deterministic Xor Automata. [Research Report] Ecole Normale Supérieure. 2010, pp.25. ⟨inria-00487031⟩



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