Kleene algebra with converse
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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The Equational Theory of Positive Relation Algebra
MOVE
in Marseille,
March 2017
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The Equational Theory of Positive Relation Algebra
PACE
in Shanghai,
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A Kleene Theorem for Petri automata
Highlights
in Brussels,
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Une introduction aux algèbres de Kleene
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in Lyon,
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(in French)
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Petri automata for Kleene Allegories
LiCS
in Kyoto,
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Petri automata for Kleene allegories
Rapido
in Paris,
June 2015
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Petri automata for Kleene allegories
Midlands Graduate School
in Sheffield,
April 2015
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Décidabilité des Treillis de Kleene sans identité
JFLA
in Val d'Ajol,
January 2015
(in French)
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Decidability of Identity-free Kleene Lattices
LAC
in Chambéry,
November 2014
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Kleene Algebra with Converse
RAMiCS
in Marienstatt,
April 2014
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Deciding Kleene Algebra with converse is PSpace-complete
GeoCal
in Bordeaux,
March 2014
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Deciding Kleene Algebra with converse is PSpace-complete
PACE
in Lyon,
February 2014
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Algèbres de Relations, Étude des algèbres de Kleene avec converse
Internship defence
in Paris,
September 2013
(Internship defence, in French)
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Equivalence of regular expressions with converse on relations
PiCoq
in Lyon,
June 2013
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Related papers | ||
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Petri automata
(in LMCS 2017)
with Damien Pous. |
More | |
| 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. |
More | |
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Petri automata for Kleene allegories
(in LICS 2015)
with Damien Pous. |
More | |
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Decidability of identity-free relational Kleene lattices
(in JFLA 2015)
with Damien Pous. |
More | |