A Coalgebraic Approach to Process Equivalence and a Coinduction Principle for Traces

Klin, Bartek

doi:10.1016/j.entcs.2004.02.029

Cited by 10 publications

(10 citation statements)

References 7 publications

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“…Subsets of T 2, i.e. T -algebras on 2, have appeared as modalities in [11]. Proposition 16 establishes that this notion of modality and the one induced by predicate liftings are equivalent.…”

Section: Classification Of Predicate Liftingsmentioning

confidence: 87%

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Expressivity of Coalgebraic Modal Logic: The Limits and Beyond

Schröder

2005

Foundations of Software Science and Computational Structures

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Abstract. Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from so-called predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, conversely, logically indistinguishable states are behaviorally equivalent depend on the existence of separating sets of predicate liftings for the signature functor at hand. Here, we provide a classification result for predicate liftings which leads to an easy criterion for the existence of such separating sets, and we give simple examples of functors that fail to admit expressive normal or monotone modal logics, respectively, or in fact an expressive (unary) modal logic at all. We then move on to polyadic modal logic, where modal operators may take more than one argument formula. We show that every accessible functor admits an expressive polyadic modal logic. Moreover, expressive polyadic modal logics are, unlike unary modal logics, compositional.

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Section: Classification Of Predicate Liftingsmentioning

confidence: 87%

“…Here, we observe that predicate liftings are equivalent to a notion of modality used in [11]; this affords an immediate overview of all possible predicate liftings of a given functor. Moreover, one obtains easy criteria which identify socalled monotone and continuous predicate liftings, respectively.…”

Section: Introductionmentioning

confidence: 99%

Expressivity of Coalgebraic Modal Logic: The Limits and Beyond

Schröder

2005

Foundations of Software Science and Computational Structures

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“…As a simple application we present the same example used by Klin in [Kli04]. We prove that any process has the same traces as its deterministic form.…”

Section: A Simple Application Examplementioning

confidence: 91%

“…But we need care when coping with infinite processes. As Klin, we use here a coalgebraic reasoning to do it, but our proof is simpler than that in [Kli04], although it is true that Klin develops his approach in a broader framework than ours.…”

Section: A Simple Application Examplementioning

confidence: 99%

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Bisimulations Up-to for the Linear Time Branching Time Spectrum

Frutos-Escrig

Rodríguez

2005

Lecture Notes in Computer Science

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Abstract. Coinductive definitions of semantics based on bisimulations have rather pleasant properties and are simple to use. In order to get coinductive characterisations of those semantic equivalences that are weaker than strong bisimulation we use a variant of the bisimulation up-to technique in which we allow the use of a given preorder relation. We prove that under some technical conditions our bisimulations up-to characterise the kernel of the given preorder. It is remarkable that the adequate orientation of the ordering relation is crucial to get this result. As a corollary, we get nice coinductive characterisations of all the axiomatic semantic equivalences in Van Glabbeek's spectrum. Although we first prove our results for finite processes, reasoning by induction, then we see, by using continuity arguments, that they are also valid for infinite (finitary) processes.

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Brzozowski’s and Up-To Algorithms for Must Testing

Bonchi¹,

Caltais²,

Pous³

et al. 2013

Programming Languages and Systems

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Checking language equivalence (or inclusion) of finite automata is a classical problem in Computer Science, which has recently received a renewed interest and found novel and more effective solutions, such as approaches based on antichains or bisimulations up-to. Several notions of equivalence (or preorder) have been proposed for the analysis of concurrent systems. Usually, the problem of checking these equivalences is reduced to checking bisimilarity. In this paper, we take a different approach and propose to adapt algorithms for language equivalence to check one prime equivalence in concurrency theory, must testing semantics. To achieve this transfer of technology from language to must semantics, we take a coalgebraic outlook at the problem.

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A Coalgebraic Approach to Process Equivalence and a Coinduction Principle for Traces

Cited by 10 publications

References 7 publications

Expressivity of Coalgebraic Modal Logic: The Limits and Beyond

Expressivity of Coalgebraic Modal Logic: The Limits and Beyond

Bisimulations Up-to for the Linear Time Branching Time Spectrum

Brzozowski’s and Up-To Algorithms for Must Testing

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