Decidability of Identityfree Kleene Lattices
LAC
in Chambéry,
November 2014
Families of binary relations are important interpretations of regular expressions, and the equivalence of two regular expressions with respect to their relational interpretations is decidable: the problem reduces to the equality of the denoted regular languages.
Putting together a few results from the literature, we first make explicit a generalisation of this reduction, for regular expressions extended with converse and intersection: instead of considering sets of words (i.e., formal languages), one has to consider sets of directed and labelled graphs.
We then focus on identityfree regular expressions with converse—a setting where the above graphs are acyclic—and we show that the corresponding equational theory is decidable. We achieve this by defining an automaton model, based on Petri Nets, to recognise these sets of acyclic graphs, and by providing an algorithm to compare such automata.
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  
Kleene Algebra with Converse
RAMiCS
in Marienstatt,
April 2014
.

More  
Deciding Kleene Algebra with converse is PSpacecomplete
GeoCal
in Bordeaux,
March 2014
.

More  
Deciding Kleene Algebra with converse is PSpacecomplete
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  
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  
Algebras of relations: from algorithms to formal proofs (in Université de Lyon 2016)  More  
Petri automata for Kleene allegories
(in LICS 2015)
with Damien Pous. 
More  
Decidability of identityfree relational Kleene lattices
(in JFLA 2015)
with Damien Pous. 
More  
Kleene algebra with converse
(in RAMICS 2014)
with Damien Pous. 
More 