Kleene algebra with converse

with Damien Pous .

conference paper, in RAMICS 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.

@inproceedings{bp14,
    title = "Kleene algebra with converse",
    author = "{Paul Brunet}, {Damien Pous}",
    year = 2014,
    booktitle = "RAMICS",
    doi = "10.1007/978-3-319-06251-8_7"
}

Links

	Permanent link
	Preprint on HAL
	Paper on Springer Link

Related talks
	The Equational Theory of Positive Relation Algebra MOVE in Marseille, March 2017.	More
	The Equational Theory of Positive Relation Algebra PACE in Shanghai, November 2016.	More
	A Kleene Theorem for Petri automata Highlights in Brussels, September 2016.	More
	Une introduction aux algèbres de Kleene Inter'Actions in Lyon, May 2016 (in French) .	More
	Petri automata for Kleene Allegories LiCS in Kyoto, July 2015.	More
	Petri automata for Kleene allegories Rapido in Paris, June 2015.	More
	Petri automata for Kleene allegories Midlands Graduate School in Sheffield, April 2015.	More
	Décidabilité des Treillis de Kleene sans identité JFLA in Val d'Ajol, January 2015 (in French) .	More
	Decidability of Identity-free Kleene Lattices LAC in Chambéry, November 2014.	More
	Kleene Algebra with Converse RAMiCS in Marienstatt, April 2014.	More
	Deciding Kleene Algebra with converse is PSpace-complete GeoCal in Bordeaux, March 2014.	More
	Deciding Kleene Algebra with converse is PSpace-complete PACE in Lyon, February 2014.	More
	Algèbres de Relations, Étude des algèbres de Kleene avec converse Internship defence in Paris, September 2013 (Internship defence, in French) .	More
	Equivalence of regular expressions with converse on relations PiCoq in Lyon, June 2013.	More
Related papers
	Petri automata (in LMCS 2017) with Damien Pous.	More
	Algebras of relations: from algorithms to formal proofs (in Université de Lyon 2016)	More
	Cardinalities of finite relations in Coq (in ITP 2016) with Insa Stucke and Damien Pous.	More
	Algorithms for Kleene algebra with converse (in JLAMP 2016) with Damien Pous.	More
	Petri automata for Kleene allegories (in LICS 2015) with Damien Pous.	More
	Decidability of identity-free relational Kleene lattices (in JFLA 2015) with Damien Pous.	More