We show that the language equivalence problem for regular and context-free
commutative grammars is coNEXP-complete. In addition, our lower bound
immediately yields further coNEXP-completeness results for equivalence problems
for communication-free Petri nets and reversal-bounded counter automata.
Moreover, we improve both lower and upper bounds for language equivalence for
exponent-sensitive commutative grammars.Comment: 21 page

Haase, Christoph

Hofman, Piotr

English

arXiv

Given two finite-state automata, are the Parikh images of the languages they generate equiva-lent? This problem was shown decidable in coNEXP by Huynh in 1985 within the more general setting of context-free commutative grammars. Huynh conjectured that a ΠP2 upper bound might be possible, and Kopczyński and To established in 2010 such an upper bound when the size of the alphabet is fixed. The contribution of this paper is to show that the language equivalence problem for regular and context-free commutative grammars is actually coNEXP-complete. In addition, our lower bound immediately yields further coNEXP-completeness results for equiv-alence problems for regular commutative expressions, reversal-bounded counter automata and communication-free Petri nets. Finally, we improve both lower and upper bounds for language equivalence for exponent-sensitive commutative grammars

Christoph Haase

Piotr Hofman

CiteSeerX

Tightening the Complexity of Equivalence Problems for Commutative Grammars∗

Given two finite-state automata, are the Parikh images of the languages they generate equivalent? This problem was shown decidable in coNEXP by Huynh in 1985 within the more general setting of context-free commutative grammars. Huynh conjectured that a Pi_2^P upper bound might be possible, and Kopczynski and To established in 2010 such an upper bound when the size of the alphabet is fixed. The contribution of this paper is to show that the language equivalence problem for regular and context-free commutative grammars is actually coNEXP-complete. In addition, our lower bound immediately yields further coNEXP-completeness results for equivalence problems for regular commutative expressions, reversal-bounded counter automata and communication-free Petri nets. Finally, we improve both lower and upper bounds for language equivalence for exponent-sensitive commutative grammars

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Tightening the Complexity of Equivalence Problems for Commutative Grammars

http://www.lsv.ens-cachan.fr/Publis/PAPERS/PDF/HH-stacs16.pdf

Tightening the Complexity of Equivalence Problems for Commutative Grammars

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