Automatic equivalence proofs for non-deterministic coalgebras

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2013
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Bonsangue, Marcello
Goriac, Eugen-Ioan
Lucanu, Dorel
Rutten, Jan
Silva, Alexandra
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Zusammenfassung

A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analog of Kleene’s theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems covered include infinite streams, deterministic automata, Mealy machines and labeled transition systems. In this paper, we present a novel algorithm to decide whether two expressions are bisimilar or not. The procedure is implemented in the automatic theorem prover CIRC, by reducing coinduction to an entailment relation between an algebraic specification and an appropriate set of equations. We illustrate the generality of the tool with three examples: infinite streams of real numbers, Mealy machines and labeled transition systems.

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004 Informatik
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Coalgebra, Algebra, Bisimilarity, Automatic reasoning
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ISO 690BONSANGUE, Marcello, Georgiana CALTAIS, Eugen-Ioan GORIAC, Dorel LUCANU, Jan RUTTEN, Alexandra SILVA, 2013. Automatic equivalence proofs for non-deterministic coalgebras. In: Science of Computer Programming. 2013, 78(9), pp. 1324-1345. ISSN 0167-6423. eISSN 1872-7964. Available under: doi: 10.1016/j.scico.2012.07.001
BibTex
@article{Bonsangue2013-09Autom-44681,
  year={2013},
  doi={10.1016/j.scico.2012.07.001},
  title={Automatic equivalence proofs for non-deterministic coalgebras},
  number={9},
  volume={78},
  issn={0167-6423},
  journal={Science of Computer Programming},
  pages={1324--1345},
  author={Bonsangue, Marcello and Caltais, Georgiana and Goriac, Eugen-Ioan and Lucanu, Dorel and Rutten, Jan and Silva, Alexandra}
}
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