Reversible Kleene lattices

Abstract : We investigate the equational theory of reversible Kleene lattices, that is algebras of languages with the regular operations (union, composition and Kleene star), together with the intersection and mirror image. Building on results by Andréka, Mikulás and Németi from 2011, we construct the free representation of this algebra. We then provide an automaton model to compare representations. These automata are adapted from Petri automata, which we introduced with Pous in 2015 to tackle a similar problem for algebras of binary relations. This allows us to show that testing the validity of equations in this algebra is decidable, and in fact ExpSpace-complete.
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Kim G. Larsen; Hans L. Bodlaender; Jean-Francois Raskin. 42nd International Symposium on Mathematical Foundations of Computer Science, Aug 2017, Aalborg, Denmark. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 83, pp.66:1--66:14, 2017, Leibniz International Proceedings in Informatics (LIPIcs). 〈http://mfcs2017.cs.aau.dk/index.shtml〉. 〈10.4230/LIPIcs.MFCS.2017.66〉
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Paul Brunet. Reversible Kleene lattices. Kim G. Larsen; Hans L. Bodlaender; Jean-Francois Raskin. 42nd International Symposium on Mathematical Foundations of Computer Science, Aug 2017, Aalborg, Denmark. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 83, pp.66:1--66:14, 2017, Leibniz International Proceedings in Informatics (LIPIcs). 〈http://mfcs2017.cs.aau.dk/index.shtml〉. 〈10.4230/LIPIcs.MFCS.2017.66〉. 〈hal-01474911v3〉

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