We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent confluence proofs. For this, we introduce the structure of higher globular Kleene algebra, a higher-dimensional generalisation of modal and concurrent Kleene algebra. We calculate a coherent Church-Rosser theorem and a coherent Newman's lemma in higher Kleene algebras by equational reasoning. We instantiate these results in the context of higher rewriting systems modelled by polygraphs.Comment: Pre-print (third version
We prove a Kleene theorem for higher-dimensional automata (HDAs). It states that the languages they ...
AbstractThe work presented here investigates the combination of Kleene algebra with the synchrony mo...
In this thesis, we study applications of rewriting theory to categorification problems and represent...
International audienceWe extend the formalisation of confluence results in Kleene algebras to a form...
We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent ...
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms t...
A coherent presentation of an n-category is a presentation by generators, relations and relations am...
We study the Horn theories of Kleene algebras and star continuous Kleene algebras, from the complexi...
International audienceThe equational theory generated by all algebras of binary relations with opera...
We prove two completeness results for Kleene algebra with a top element, with respect to languages a...
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms t...
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to pro...
We study Higher-Order Rewrite Systems (HRSs) which extend term rewriting to -terms. HRSs can descri...
Kleene algebras provide a convenient and powerful algebraic axiomatisation of a complete lattice tha...
Kleene algebras provide a convenient and powerful algebraic axiomatisation of a complete lattice tha...
We prove a Kleene theorem for higher-dimensional automata (HDAs). It states that the languages they ...
AbstractThe work presented here investigates the combination of Kleene algebra with the synchrony mo...
In this thesis, we study applications of rewriting theory to categorification problems and represent...
International audienceWe extend the formalisation of confluence results in Kleene algebras to a form...
We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent ...
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms t...
A coherent presentation of an n-category is a presentation by generators, relations and relations am...
We study the Horn theories of Kleene algebras and star continuous Kleene algebras, from the complexi...
International audienceThe equational theory generated by all algebras of binary relations with opera...
We prove two completeness results for Kleene algebra with a top element, with respect to languages a...
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms t...
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to pro...
We study Higher-Order Rewrite Systems (HRSs) which extend term rewriting to -terms. HRSs can descri...
Kleene algebras provide a convenient and powerful algebraic axiomatisation of a complete lattice tha...
Kleene algebras provide a convenient and powerful algebraic axiomatisation of a complete lattice tha...
We prove a Kleene theorem for higher-dimensional automata (HDAs). It states that the languages they ...
AbstractThe work presented here investigates the combination of Kleene algebra with the synchrony mo...
In this thesis, we study applications of rewriting theory to categorification problems and represent...