An Axiomatization of Strong Distribution Bisimulation for a Language with a Parallel Operator and Probabilistic Choice

Groote, Jan Friso; Vink, Erik P. de

doi:10.1007/978-3-030-30985-5_26

Cited by 5 publications

(3 citation statements)

References 28 publications

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“…The substantial differences in the considered probabilistic models (see [39] for a survey) prevent us from discussing these results in detail. Yet, we remark that we can find studies on strong probabilistic semantics [7,20,47,50,56,57,68,70], weak probabilistic semantics [18,19,46], as well as on metric semantics [38]. Further studies in this direction are encouraged by recent achievements on probabilistic branching semantics [32,33] and behavioural metrics [30,31].…”

Section: Introducing Silent Stepsmentioning

confidence: 91%

In search of lost time: Axiomatising parallel composition in process algebras

Aceto¹,

Anastasiadi²,

Castiglioni³

et al. 2021

Preprint

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This survey reviews some of the most recent achievements in the saga of the axiomatisation of parallel composition, along with some classic results. We focus on the recursion, relabelling and restriction free fragment of CCS and we discuss the solutions to three problems that were open for many years. The first problem concerns the status of Bergstra and Klop's auxiliary operators left merge and communication merge in the finite axiomatisation of parallel composition modulo bisimiliarity: We argue that, under some natural assumptions, the addition of a single auxiliary binary operator to CCS does not yield a finite axiomatisation of bisimilarity. Then we delineate the boundary between finite and non-finite axiomatisability of the congruences in van Glabbeek's linear timebranching time spectrum over CCS. Finally, we present a novel result to the effect that rooted weak bisimilarity has no finite complete axiomatisation over CCS.

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Section: Introducing Silent Stepsmentioning

confidence: 91%

In search of lost time: Axiomatising parallel composition in process algebras

Aceto¹,

Anastasiadi²,

Castiglioni³

et al. 2021

Preprint

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“…We propose the notion of a stable distribution and show that every distribution can be unfolded into a stable distribution by chasing its (partial) τ-transitions. Our framework, including the notion of branching probabilistic bisimulation, builds on that of [19,16].…”

Section: Introductionmentioning

confidence: 99%

“…Another trait of the current paper, as in [19,16], is that distributions are taken as semantic foundation for bisimilarity, rather than seeing bisimilarity primarily as an equivalence relation on non-deterministic processes, which is subsequently lifted to an equivalence relation on distributions, as is the case for the notion of branching probabilistic bisimilarity of [27,26] and also of [2,1]. The idea to consider distributions as first-class citizens for probabilistic bisimilarity stems from [11].…”

Section: Introductionmentioning

confidence: 99%

A Cancellation Law for Probabilistic Processes

van Glabbeek,

Groote,

de Vink

2023

Electron. Proc. Theor. Comput. Sci.

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We show a cancellation property for probabilistic choice. If µ ⊕ ρ and ν ⊕ ρ are branching probabilistic bisimilar, then µ and ν are also branching probabilistic bisimilar. We do this in the setting of a basic process language involving non-deterministic and probabilistic choice and define branching probabilistic bisimilarity on distributions. Despite the fact that the cancellation property is very elegant and concise, we failed to provide a short and natural combinatorial proof. Instead we provide a proof using metric topology. Our major lemma is that every distribution can be unfolded into an equivalent stable distribution, where the topological arguments are required to deal with uncountable branching.

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