Generic Trace Semantics via Coinduction

Hasuo, Ichiro; Jacobs, Bart; Sokolova, Ana

doi:10.2168/lmcs-3(4:11)2007

Cited by 122 publications

(322 citation statements)

References 52 publications

(96 reference statements)

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“…Moreover ≈ T F coincides with the trace semantics of probabilistic transition systems defined in [19] (see Section 7.2 of [23]). …”

Section: Structured Moore Automatamentioning

confidence: 75%

“…The exact relationship between these two approaches has been studied in [23] (and, indirectly, it could be deduced from [6] and [27]). It is worth to remark that many of our examples do not fit the framework in [19]: for instance, the exception, the side effect, the full-probability and the interactive output monads do not fulfill their requirements (the first three do not have a bottom element and the latter is not commutative). Moreover, we also note that the example of partial Mealy machines is not purely trace-like, as all the examples in [19].…”

Section: Discussionmentioning

confidence: 97%

“…Some of the aforementioned examples can also be coalgebraically characterized in the framework of [19,18]. There, instead of considering F T -coalgebras on Set and F * -coalgebras on Set T (the Eilenberg-Moore category), T G-coalgebras on Set and G-coalgebras on Set T (the Kleisli category) are studied.…”

Section: Discussionmentioning

confidence: 99%

“…There, instead of considering F T -coalgebras on Set and F * -coalgebras on Set T (the Eilenberg-Moore category), T G-coalgebras on Set and G-coalgebras on Set T (the Kleisli category) are studied. The main theorem of [19] states that under certain assumptions, the initial G-algebra is the final G-coalgebra that characterizes (generalized) trace equivalence. The exact relationship between these two approaches has been studied in [23] (and, indirectly, it could be deduced from [6] and [27]).…”

Section: Discussionmentioning

confidence: 99%

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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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“…Moreover ≈ T F coincides with the trace semantics of probabilistic transition systems defined in [19] (see Section 7.2 of [23]). …”

Section: Structured Moore Automatamentioning

confidence: 75%

Section: Discussionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Generalizing determinization from automata to coalgebras

Silva¹,

Bonchi²,

Bonsangue³

et al. 2013

Logical Methods in Computer Science

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show abstract

“…Coalgebraically, trace semantics has been studied in [14] and, more recently, in [22]. The latter contains a generalization of the classical powerset construction to a more general class of systems.…”

Section: Lemma 1 (Compositionality) For Reo Automatamentioning

confidence: 99%

A Specification Language for Reo Connectors

Silva

2012

Fundamentals of Software Engineering

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Abstract. Recent approaches to component-based software engineering employ coordinating connectors to compose components into software systems. Reo is a model of component coordination, wherein complex connectors are constructed by composing various types of primitive channels. Reo automata are a simple and intuitive formal model of context-dependent connectors, which provided a compositional semantics for Reo. In this paper, we study Reo automata from a coalgebraic perspective. This enables us to apply the recently developed coalgebraic theory of generalized regular expressions in order to derive a specification language, tailor-made for Reo automata, and sound and complete axiomatizations with respect to three distinct notions of equivalence: (coalgebraic) bisimilarity, the bisimulation notion studied in the original papers on Reo automata and trace equivalence. The obtained language is simple, but nonetheless expressive enough to specify all possible finite Reo automata. Moreover, it comes equipped with a Kleene-like theorem: we provide algorithms to translate expressions to Reo automata and, conversely, to compute an expression equivalent to a state in a Reo automaton.

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Categorical Büchi and Parity Conditions via Alternating Fixed Points of Functors

Urabe

Hasuo

2018

Coalgebraic Methods in Computer Science

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Categorical studies of recursive data structures and their associated reasoning principles have mostly focused on two extremes: initial algebras and induction, and final coalgebras and coinduction. In this paper we study their in-betweens. We formalize notions of alternating fixed points of functors using constructions that are similar to that of free monads. We find their use in categorical modeling of accepting run trees under the Büchi and parity acceptance condition. This modeling abstracts away from states of an automaton; it can thus be thought of as the "behaviors" of systems with the Büchi or parity conditions, in a way that follows the tradition of coalgebraic modeling of system behaviors.

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Generic Trace Semantics via Coinduction

Cited by 122 publications

References 52 publications

Generalizing determinization from automata to coalgebras

Generalizing determinization from automata to coalgebras

A Specification Language for Reo Connectors

Categorical Büchi and Parity Conditions via Alternating Fixed Points of Functors

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