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Lax Bialgebras and Up-To Techniques for Weak Bisimulations

Authors Filippo Bonchi, Daniela Petrisan, Damien Pous, Jurriaan Rot

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Filippo Bonchi
Daniela Petrisan
Damien Pous
Jurriaan Rot

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Filippo Bonchi, Daniela Petrisan, Damien Pous, and Jurriaan Rot. Lax Bialgebras and Up-To Techniques for Weak Bisimulations. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 240-253, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.CONCUR.2015.240

Abstract

Up-to techniques are useful tools for optimising proofs of behavioural equivalence of processes. Bisimulations up-to context can be safely used in any language specified by GSOS rules. We showed this result in a previous paper by exploiting the well-known observation by Turi and Plotkin that such languages form bialgebras. In this paper, we prove the soundness of up-to contextual closure for weak bisimulations of systems specified by cool rule formats, as defined by Bloom to ensure congruence of weak bisimilarity. However, the weak transition systems obtained from such cool rules give rise to lax bialgebras, rather than to bialgebras. Hence, to reach our goal, we extend our previously developed categorical framework to an ordered setting.

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Keywords
  • Up-to techniques
  • weak bisimulation
  • (lax) bialgebras

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