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Tightening the Complexity of Equivalence Problems for Commutative Grammars Haase, Christoph Hofman, Piotr language equivalence commutative grammars presburger arithmetic semi-linear sets petri nets 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Christoph Haase and Piotr Hofman 2016 Is Part Of LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2016.41 urn:nbn:de:0030-drops-57422 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.41 eng https://creativecommons.org/licenses/by/3.0/legalcode