Publicação
Sound and complete axiomatizations of coalgebraic language equivalence
| Resumo: | Coalgebras provide a uniform framework for studying dynamical systems, including several types of automata. In this article, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalized powerset construction that determinizes coalgebras. We show that soundness and completeness are established by proving that expressions modulo axioms of a calculus form the rational fixpoint of the given type functor. Our main result is that the rational fixpoint of the functor FT, where T is a monad describing the branching of the systems (e.g., non-determinism, weights, probability, etc.), has as a quotient the rational fixpoint of the determinized type functor F, a lifting of F to the category of T-algebras. We apply our framework to the concrete example of weighted automata, for which we present a new sound and complete calculus for weighted language equivalence. As a special case, we obtain nondeterministic automata in which we recover Rabinovich’s sound and complete calculus for language equivalence. |
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| Autores principais: | Bonsangue, Marcello |
| Outros Autores: | Milius, Stefan; Silva, Alexandra M. |
| Assunto: | Coalgebra Language Regular expressions Trace Weighted automata |
| Ano: | 2013 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | Coalgebras provide a uniform framework for studying dynamical systems, including several types of automata. In this article, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalized powerset construction that determinizes coalgebras. We show that soundness and completeness are established by proving that expressions modulo axioms of a calculus form the rational fixpoint of the given type functor. Our main result is that the rational fixpoint of the functor FT, where T is a monad describing the branching of the systems (e.g., non-determinism, weights, probability, etc.), has as a quotient the rational fixpoint of the determinized type functor F, a lifting of F to the category of T-algebras. We apply our framework to the concrete example of weighted automata, for which we present a new sound and complete calculus for weighted language equivalence. As a special case, we obtain nondeterministic automata in which we recover Rabinovich’s sound and complete calculus for language equivalence. |
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