Kleene Algebra with Converse
RAMiCS
in Marienstatt,
April 2014
The equational theory generated by all algebras of binary relations with operations of union, composition, converse and reflexive transitive closure was studied by Bernátsky, Bloom, Ésik, and Stefanescu in 1995. We reformulate some of their proofs in syntactic and elementary terms, and we provide a new algorithm to decide the corresponding theory. This algorithm is both simpler and more efficient; it relies on an alternative automata construction, that allows us to prove that the considered equational theory lies in the complexity class PSpace.
Specific regular languages appear at various places in the proofs. Those proofs were made tractable by considering appropriate automata recognising those languages, and exploiting symmetries in those automata.
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Related papers | ||
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Petri automata
(in LMCS 2017)
with Damien Pous. |
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| Algebras of relations: from algorithms to formal proofs (in Université de Lyon 2016) | More | |
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Cardinalities of finite relations in Coq
(in ITP 2016)
with Insa Stucke and Damien Pous. |
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Algorithms for Kleene algebra with converse
(in JLAMP 2016)
with Damien Pous. |
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Petri automata for Kleene allegories
(in LICS 2015)
with Damien Pous. |
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Decidability of identity-free relational Kleene lattices
(in JFLA 2015)
with Damien Pous. |
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Kleene algebra with converse
(in RAMICS 2014)
with Damien Pous. |
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