An Overview of Probabilistic Process Algebras and Their Equivalences

López, Natalia; Núñez, Manuel

doi:10.1007/978-3-540-24611-4_3

Cited by 32 publications

(21 citation statements)

References 43 publications

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“…Bisimulation equivalence allows one to relate bisimilar systems and to reduce the state space of a system by combining bisimilar states to generate a quotient system with an equivalent behavior but with fewer states. In the past two decades, bisimulation has been considerably extended to arXiv:1012.2148v1 [cs.AI] 10 Dec 2010 probabilistic and stochastic systems (see, for example, [2], [3], [16], [22], [26] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Bisimulations for Fuzzy-Transition Systems

Cao

Chen

Kerre

2011

IEEE Trans. Fuzzy Syst.

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Abstract-There has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems, but the comparison at this level is too coarse. Recently, a finer behavioral measure, bisimulation, has been introduced to fuzzy finite automata. However, the results obtained are applicable only to finite-state systems. In this paper, we consider bisimulation for general fuzzy systems which may be infinite-state or infiniteevent, by modeling them as fuzzy transition systems. To help understand and check bisimulation, we characterize it in three ways by enumerating whole transitions, comparing individual transitions, and using a monotonic function. In addition, we address composition operations, subsystems, quotients, and homomorphisms of fuzzy transition systems and discuss their properties connected with bisimulation. The results presented here are useful for comparing the behavior of general fuzzy systems. In particular, this makes it possible to relate an infinite fuzzy system to a finite one, which is easier to analyze, with the same behavior.

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Section: Introductionmentioning

confidence: 99%

Bisimulations for Fuzzy-Transition Systems

Cao

Chen

Kerre

2011

IEEE Trans. Fuzzy Syst.

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“…To add probabilities to CCS calculus we will follow alternating model (the approach presented in [HJ90]) which is neither reactive nor generative nor stratified (see [LN04]). Probabilistic transitions are not associated with actions but they are labeled with probabilities.…”

Section: Probabilistic Process Algebramentioning

confidence: 99%

Differential Privacy and Security

Gruska

2016

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“…We now describe some of the implementation relations, though it should be noted that we do not cover all implementation relations discussed in the literature including some recent extensions with probabilities (see, for example, [López and Núñez 2004]). 6.3.1 Trace preorder.…”

Section: ≤ R S Iff ∀ T ∈ Lts : Runs(t I) ⊆ Runs(t S)mentioning

confidence: 99%