Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages

Latella, Diego; Massink, Mieke; Vink, Erik P. de

doi:10.4204/eptcs.93.2

Cited by 5 publications

(19 citation statements)

References 26 publications

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“…As a consequence of the general result relating FuTS bisimulation and behavioral equivalence we obtain, in a systematic way, a coalgebraic underpinning of all quantitative bisimulations discussed.with non-determinism as well as with discrete probability distributions over behaviours-and for their comparison with other recent approaches to a uniform treatment of SPC semantics, e.g. Rated Transition Systems [19], Rate Transition Systems [10], Weighted Transition Systems [18], and ULTraS [6].In [24] we proposed a coalgebraic view of FuTS involving functors FS(·, R ), for R a semiring, in place to deal with quantities. Here, for a set of states S, we use FS(S, R ) to denote the set of all finitely supported functions from S to R. Discrete probability distributions are a typical example of such a function space.…”

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confidence: 86%

“…Note, this excludes by no means the treatment of non-deterministic systems. Below and in [11,24] it has been shown that the class of FuTS given by the definition above is sufficiently rich to deal with all the major stochastic process description languages and their underlying semantic models.…”

Section: Definitionmentioning

confidence: 99%

“…In [24] we proposed a coalgebraic view of FuTS involving functors FS(·, R ), for R a semiring, in place to deal with quantities. Here, for a set of states S, we use FS(S, R ) to denote the set of all finitely supported functions from S to R. Discrete probability distributions are a typical example of such a function space.…”

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confidence: 99%

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A Definition Scheme for Quantitative Bisimulation

Latella

Massink

Vink

2015

Electron. Proc. Theor. Comput. Sci.

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FuTS, state-to-function transition systems are generalizations of labeled transition systems and of familiar notions of quantitative semantical models as continuous-time Markov chains, interactive Markov chains, and Markov automata. A general scheme for the definition of a notion of strong bisimulation associated with a FuTS is proposed. It is shown that this notion of bisimulation for a FuTS coincides with the coalgebraic notion of behavioral equivalence associated to the functor on Set given by the type of the FuTS. For a series of concrete quantitative semantical models the notion of bisimulation as reported in the literature is proven to coincide with the notion of quantitative bisimulation obtained from the scheme. The comparison includes models with orthogonal behaviour, like interactive Markov chains, and with multiple levels of behavior, like Markov automata. As a consequence of the general result relating FuTS bisimulation and behavioral equivalence we obtain, in a systematic way, a coalgebraic underpinning of all quantitative bisimulations discussed.

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confidence: 86%

Section: Definitionmentioning

confidence: 99%

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A Definition Scheme for Quantitative Bisimulation

Latella

Massink

Vink

2015

Electron. Proc. Theor. Comput. Sci.

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“…The correspondence result shown in [Latella et al 2012] sets the basis for a systematic study of SPCs, within the FuTS framework, based on category theory, and in particular within the coalgebraic framework, similar to what has been done for probabilistic models in [Bartels 2002;Bartels et al 2003;Sokolova and de Vink 2004], for Rated TSs by Klin and Sassone [2008] and WTSs [Klin 2009]. We think this is a promising line of future research which should be undertaken for FuTSs; in particular, the relationship between WTSs Weighted GSOS on one hand and FuTSs and related PCs sematics rules on the other seems an interesting line of research.…”

Section: Discussionmentioning

confidence: 99%

“…In [Latella et al 2012] the notion of bisimulation induced by FuTSs is addressed from a co-algebraic perspective. A correspondence result is proven stating that FuTS-bisimulation coincides with the behavioral equivalence of the associated functor.…”

Section: · 33mentioning

confidence: 99%

A uniform definition of stochastic process calculi

et al. 2013

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We introduce a unifying framework to provide the semantics of process algebras, including their quantitative variants useful for modeling quantitative aspects of behaviors. The unifying framework is then used to describe some of the most representative stochastic process algebras. This provides a general and clear support for an understanding of their similarities and differences. The framework is based on State to Function Labeled Transition Systems, FuTSs for short, that are state-transition structures where each transition is a triple of the form (s, α, P). The first and the second components are the source state, s, and the label, α, of the transition, while the third component is the continuation function, P, associating a value of a suitable type to each state s . For example, in the case of stochastic process algebras the value of the continuation function on s represents the rate of the negative exponential distribution characterizing the duration/delay of the action performed to reach state s from s. We first provide the semantics of a simple formalism used to describe Continuous-Time Markov Chains, then we model a number of process algebras that permit parallel composition of models according to the two main interaction paradigms (multiparty and one-to-one synchronization). Finally, we deal with formalisms where actions and rates are kept separate and address the issues related to the co-existence of stochastic, probabilistic, and non-deterministic behaviors. For each formalism, we establish the formal correspondence between the FuTSs semantics and its original semantics.

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Coalgebraic Weak Bisimulation from Recursive Equations over Monads

Goncharov

Pattinson

2014

Automata, Languages, and Programming

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Abstract. Strong bisimulation for labelled transition systems is one of the most fundamental equivalences in process algebra, and has been generalised to numerous classes of systems that exhibit richer transition behaviour. Nearly all of the ensuing notions are instances of the more general notion of coalgebraic bisimulation. Weak bisimulation, however, has so far been much less amenable to a coalgebraic treatment.Here we attempt to close this gap by giving a coalgebraic treatment of (parametrized) weak equivalences, including weak bisimulation. Our analysis requires that the functor defining the transition type of the system is based on a suitable order-enriched monad, which allows us to capture weak equivalences by least fixpoints of recursive equations. Our notion is in agreement with existing notions of weak bisimulations for labelled transition systems, probabilistic and weighted systems, and simple Segala systems.

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Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages

Cited by 5 publications

References 26 publications

A Definition Scheme for Quantitative Bisimulation

A Definition Scheme for Quantitative Bisimulation

A uniform definition of stochastic process calculi

Coalgebraic Weak Bisimulation from Recursive Equations over Monads

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