Introduction to Bisimulation and Coinduction

Sangiorgi, Davide

doi:10.1017/cbo9780511777110

Cited by 214 publications

(208 citation statements)

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“…For instance, up-to weak bisimilarity and up-to transitive closure are no longer sound for weak bisimulations. And up-to context has to be restricted: the external choice from CCS cannot be freely used [46].…”

Section: Contributions and Applicationsmentioning

confidence: 99%

A general account of coinduction up-to

et al. 2016

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Bisimulation up-to enhances the coinductive proof method for bisimilarity, providing efficient proof techniques for checking properties of different kinds of systems. We prove the soundness of such techniques in a fibrational setting, building on the seminal work of Hermida and Jacobs. This allows us to systematically obtain up-to techniques not only for bisimilarity but for a large class of coinductive predicates modeled as coalgebras. The fact that bisimulations up to context can be safely used in any language specified by GSOS rules can also be seen as an instance of our framework, using the well-known observation by Turi and Plotkin that such languages form bialgebras. In the second part of the paper, we provide a new categorical treatment of weak bisimilarity on labeled transition systems and we prove the soundness of up-to context for weak bisimulations of systems specified by cool rule formats, as defined by Bloom to ensure congruence of weak bisimilarity. 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 the categorical framework developed in the first part to an ordered setting. B Daniela Petrişan

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Section: Contributions and Applicationsmentioning

confidence: 99%

A general account of coinduction up-to

et al. 2016

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“…From a theoretical standpoint, the characterisation in terms of actions relabelling seems to make justice to this classic process algebra operator, which has been oftentimes neglected in recent developments of this field (see [20] for a discussion). The property of partition-preservation for a relabelling function presented in this paper is less restrictive than injectivity, as required for standard bisimulation results; yet it permits compositional reasoning for our dimmed relations.…”

Section: Resultsmentioning

confidence: 99%

Dimming Relations for the Efficient Analysis of Concurrent Systems via Action Abstraction

Nicola

Iacobelli

Tribastone

2014

Formal Techniques for Distributed Objects, Components, and Systems

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Abstract. We study models of concurrency based on labelled transition systems where abstractions are induced by a partition of the action set. We introduce dimming relations, i.e., notions of behavioural equivalence which are able to relate two models if they can match each other's actions whenever they are in the same partition block. We show applicability to a number of situations of practical interest which are apparently heterogeneous but exhibit similar behaviors although manifested via different actions. Dimming relations make the models more homogeneous by collapsing such distinct actions into the same partition block. With our examples, we show how these abstractions permit reducing the state-space complexity from exponential to polynomial in the number of concurrent processes.

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“…By the Knaster-Tarski theorem, if P is a complete join semilattice and f is monotone, then lfp (f ) exists (e.g., [12,40]). Slightly more generally, lfp (f ) exists even if P is a dcpo with a least element ⊥, and f : P → P is monotone.…”

Section: Partial Ordersmentioning

confidence: 99%

Structural congruence for bialgebraic semantics

Rot¹,

Bonsangue²

2016

Journal of Logical and Algebraic Methods in Programming

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It was observed by Turi and Plotkin that structural operational semantics can be studied at the level of universal coalgebra, providing specification formats for well-behaved operations on many different types of systems. We extend this framework with non-structural assignment rules which can express, for example, the syntactic format for structural congruences proposed by Mousavi and Reniers. Our main result is that the operational model of such an extended specification is well-behaved, in the sense that bisimilarity is a congruence and that bisimulation-up-to techniques are sound.

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Introduction to Bisimulation and Coinduction

Cited by 214 publications

References 100 publications

A general account of coinduction up-to

A general account of coinduction up-to

Dimming Relations for the Efficient Analysis of Concurrent Systems via Action Abstraction

Structural congruence for bialgebraic semantics

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