Bisimulation and Coinduction Enhancements: A Historical Perspective

Pous, Damien; Sangiorgi, Davide

doi:10.1007/s00165-019-00497-w

Cited by 14 publications

(7 citation statements)

References 89 publications

(102 reference statements)

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“…Enhancements of corecursion schemes may also be examined using the generalised powerset construction [Silva et al 2010]. For the more details on coinductive enhancements, we refer to the technical survey [Pous and Sangiorgi 2012] and to the historical review [Pous and Sangiorgi 2019].…”

Section: Comparisons and Related Workmentioning

confidence: 99%

From enhanced coinduction towards enhanced induction

Sangiorgi

2022

Proc. ACM Program. Lang.

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There exist a rich and well-developed theory of enhancements of the coinduction proof method, widely used on behavioural relations such as bisimilarity. We study how to develop an analogous theory for inductive behaviour relations, i.e., relations defined from inductive observables. Similarly to the coinductive setting, our theory makes use of (semi)-progressions of the form R->F(R), where R is a relation on processes and F is a function on relations, meaning that there is an appropriate match on the transitions that the processes in R can perform in which the process derivatives are in F(R). For a given preorder, an enhancement corresponds to a sound function, i.e., one for which R->F(R) implies that R is contained in the preorder; and similarly for equivalences. We introduce weights on the observables of an inductive relation, and a weight-preserving condition on functions that guarantees soundness. We show that the class of functions contains non-trivial functions and enjoys closure properties with respect to desirable function constructors, so to be able to derive sophisticated sound functions (and hence sophisticated proof techniques) from simpler ones. We consider both strong semantics (in which all actions are treated equally) and weak semantics (in which one abstracts from internal transitions). We test our enhancements on a few non-trivial examples.

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Section: Comparisons and Related Workmentioning

confidence: 99%

From enhanced coinduction towards enhanced induction

Sangiorgi

2022

Proc. ACM Program. Lang.

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“…The present article provides a retrospective account of 40 years of research in equivalence-checking techniques for concurrent systems. Compared to prior surveys on bisimulations [406] [20], we focus here on the design of algorithms and software tools for the implementation of bisimulations on finite-state systems, leaving aside all aspects related to theorem proving -see [364] for a survey on bisimulation as a proof method. The article is organized chronologically: Sections 2-5 present the main achievements done during the 1980s, 1990s, 2000s, and 2010s decades, respectively, and Section 6 gives a few concluding remarks.…”

Section: Introductionmentioning

confidence: 99%

Equivalence Checking 40 Years After: A Review of Bisimulation Tools

Garavel

Lang

2022

Lecture Notes in Computer Science

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Equivalence checking is a formal verification approach that consists in proving that two programs or models are related modulo some equivalence relation, or that one is included in the other modulo some preorder relation. In the case of concurrent systems, which are often represented using labelled transition systems, the relations used for equivalence checking are bisimulations and their simulation preorders. In the case of probabilistic or stochastic systems, which are usually represented using Markov chains, the relations used for equivalence checking are lumpability, probabilistic and stochastic equivalences, and their associated preorders. The present article provides a synthetic overview of 40 years of research in the design of algorithms and software tools for equivalence checking.

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“…• Conditional bisimulation relations tend to be very large -often infinite in size. To obtain possibly substantial reductions of proof obligations in a bisimulation proof, we propose an up-to context technique (for up-to techniques and their history see [PS19]). In particular, it can replace an infinite conditional bisimulation relation by a possibly finite bisimulation up-to context, which provides a witness for bisimilarity.…”

Section: Introductionmentioning

confidence: 99%

Conditional Bisimilarity for Reactive Systems

Hülsbusch¹,

König²,

Küpper³

et al. 2022

Logical Methods in Computer Science

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Reactive systems \`a la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to obtain a compositional semantics. We enrich the notion of reactive systems by conditions on two levels: first, as in earlier work, we consider rules enriched with application conditions and second, we investigate the notion of conditional bisimilarity. Conditional bisimilarity allows us to say that two system states are bisimilar provided that the environment satisfies a given condition. We present several equivalent definitions of conditional bisimilarity, including one that is useful for concrete proofs and that employs an up-to-context technique, and we compare with related behavioural equivalences. We consider examples based on DPO graph rewriting, an instantiation of reactive systems.

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Bisimulation and Coinduction Enhancements: A Historical Perspective

Cited by 14 publications

References 89 publications

From enhanced coinduction towards enhanced induction

From enhanced coinduction towards enhanced induction

Equivalence Checking 40 Years After: A Review of Bisimulation Tools

Conditional Bisimilarity for Reactive Systems

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