A Coalgebraic Characterization of Behaviours in the Linear Time – Branching Time Spectrum

Monteiro, Luís

doi:10.1007/978-3-642-03429-9_17

Cited by 7 publications

(5 citation statements)

References 2 publications

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“…For commutative effect monads M , another way of extending Turi and Plotkin's framework may be to lift both syntax and behaviour functors into the Kleisli category Kl(M ) and use it as the base category (rather than splitting the approach as we have done). An application might be trace semantics for CCS-like languages, as in [13].…”

Section: Resultsmentioning

confidence: 99%

Comodels and Effects in Mathematical Operational Semantics

Abou-Saleh

Pattinson

2013

Lecture Notes in Computer Science

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In the mid-nineties, Turi and Plotkin gave an elegant categorical treatment of denotational and operational semantics for process algebra-like languages, proving compositionality and adequacy by defining operational semantics as a distributive law of syntax over behaviour. However, its applications to stateful or effectful languages, incorporating (co)models of a countable Lawvere theory, have been elusive so far. We make some progress towards a coalgebraic treatment of such languages, proposing a congruence format related to the evaluation-in-context paradigm. We formalise the denotational semantics in suitable Kleisli categories, and prove adequacy and compositionality of the semantic theory under this congruence format.

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Section: Resultsmentioning

confidence: 99%

Comodels and Effects in Mathematical Operational Semantics

Abou-Saleh

Pattinson

2013

Lecture Notes in Computer Science

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“…The approach in (Monteiro 2008) is based on an abstract notion of "behaviour object" that has similar properties with final objects. It is not clear, however, how this approach could be modularly extended so to treat probabilistic decorated traces.…”

Section: Discussionmentioning

confidence: 99%

“…A coalgebraic characterization of the spectrum, not based on the powerset construction, was attempted in Monteiro (2008). The approach in Monteiro (2008) is based on an abstract notion of 'behaviour object' that has similar properties with final objects. It is not clear, however, how this approach could be modularly extended so to treat probabilistic decorated traces.…”

Section: Discussionmentioning

confidence: 99%

A coalgebraic view on decorated traces

Bonchi

Bonsangue

Caltais

et al. 2014

Math. Struct. Comp. Sci.

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In concurrency theory, various semantic equivalences on transition systems are based on traces decorated with some additional observations, generally referred to as decorated traces. Using the generalized powerset construction, recently introduced by a subset of the authors (Silva, Bonchi, Bonsangue & Rutten 2010), we give a coalgebraic presentation of decorated trace semantics. The latter include ready, failure, (complete) trace, possible-futures, ready trace and failure trace semantics for labeled transition systems, and ready, (maximal) failure and (maximal) trace semantics for generative probabilistic systems. This yields a uniform notion of minimal representatives for the various decorated trace equivalences, in terms of final Moore automata. As a consequence, proofs of decorated trace equivalence can be given by coinduction, using different types of (Moore-) bisimulation (up-to context).

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“…In [35], it is shown a coalgebraic characterization of traces semantics (for LTS's) employing Kleisli categories. More recently, [33] have provided a characterization of trace, failure and ready semantics by mean of "behaviour objects". Another coalgebraic approach [26] relies on "test-suite" that, intuitively, are fragments of Hennessy-Milner logic.…”

Section: Beyond Bisimilarity and Tracesmentioning

confidence: 99%

Generalizing determinization from automata to coalgebras

Silva¹,

Bonchi²,

Bonsangue³

et al. 2013

Logical Methods in Computer Science

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Abstract. The powerset construction is a standard method for converting a nondeterministic automaton into a deterministic one recognizing the same language. In this paper, we lift the powerset construction from automata to the more general framework of coalgebras with structured state spaces. Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor F determines both the type of systems (F -coalgebras) and a notion of behavioural equivalence (∼F ) amongst them. Many types of transition systems and their equivalences can be captured by a functor F . For example, for deterministic automata the derived equivalence is language equivalence, while for non-deterministic automata it is ordinary bisimilarity.We give several examples of applications of our generalized determinization construction, including partial Mealy machines, (structured) Moore automata, Rabin probabilistic automata, and, somewhat surprisingly, even pushdown automata. To further witness the generality of the approach we show how to characterize coalgebraically several equivalences which have been object of interest in the concurrency community, such as failure or ready semantics. ACM CCS

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A Coalgebraic Characterization of Behaviours in the Linear Time – Branching Time Spectrum

Cited by 7 publications

References 2 publications

Comodels and Effects in Mathematical Operational Semantics

Comodels and Effects in Mathematical Operational Semantics

A coalgebraic view on decorated traces

Generalizing determinization from automata to coalgebras

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