Probabilistic simulations for probabilistic processes

Segala, Roberto; Lynch, Nancy

doi:10.1007/bfb0015027

Cited by 204 publications

(218 citation statements)

References 18 publications

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“…For these, the types are used to identify a class of nondeterministic probabilistic behaviours which can preserve the compositionality of the parallel operator in the framework of event structures. The authors claim to perform an initial step towards a good typing discipline for probabilistic name passing by employing Segala automata [18] and probabilistic event structures. In comparison with them, we simplify the approach and work directly with processes, giving a probabilistic typing in the context of multiparty session types.…”

Section: Resultsmentioning

confidence: 99%

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Probabilities in Session Types

Aman

Ciobanu

2019

Electron. Proc. Theor. Comput. Sci.

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This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing system which extends the multiparty session types in order to deal also with probabilistic behaviours. The calculus and its typing system are motivated and illustrated by a running example.

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Section: Resultsmentioning

confidence: 99%

“…An important feature of a probabilistic model is given by the distinction between nondeterministic and probabilistic choices [18]. The nondeterministic choices refer to the choices made by an external process, while probabilistic choices are choices made internally by the process (not under control of an external process).…”

Section: Introductionmentioning

confidence: 99%

Probabilities in Session Types

Aman

Ciobanu

2019

Electron. Proc. Theor. Comput. Sci.

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“…Another possible extension of our work contains probabilistic systems, for example the probabilistic automata of [43]. A possible starting point for this is [49] which uses simple stochastic games to compute probabilistic bisimilarity.…”

Section: Discussionmentioning

confidence: 99%

“…A number of quantitative models have hence been developed: probabilistic automata [43], stochastic process algebras [36], timed automata [2], hybrid automata [1], timed variants of Petri nets [30,42], continuous-time Markov chains [44], etc. Similarly, there is a number of specification formalisms for expressing quantitative properties: timed computation tree logic [35], probabilistic computation tree logic [31], metric temporal logic [37], stochastic continuous logic [3], etc.…”

Section: Introductionmentioning

confidence: 99%

Computing Branching Distances Using Quantitative Games

Fahrenberg

Legay

Quaas

2019

Theoretical Aspects of Computing – ICTAC 2019

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We lay out a general method for computing branching distances between labeled transition systems. We translate the quantitative games used for defining these distances to other, path-building games which are amenable to methods from the theory of quantitative games. We then show for all common types of branching distances how the resulting path-building games can be solved. In the end, we achieve a method which can be used to compute all branching distances in the linear-time-branching-time spectrum.

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“…There have been also several results on compositional verification of stochastic models. Similarity relations over finite-state stochastic systems have been studied either via exact notions of probabilistic (bi)simulation relations [LS91], [SL95], or approximate versions [DLT08], [DAK12]. Compositional modelling and analysis for the safety verification of stochastic hybrid systems are investigated in [HHHK13] in which random behaviour occurs only over the discrete components.…”

Section: Introductionmentioning

confidence: 99%

Compositional abstraction-based synthesis for networks of stochastic switched systems

Lavaei

Soudjani

2020

Automatica

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In this paper, we provide a compositional approach for constructing finite abstractions (a.k.a. finite Markov decision processes (MDPs)) of interconnected discrete-time stochastic switched systems. The proposed framework is based on a notion of stochastic simulation functions, using which one can employ an abstract system as a substitution of the original one in the controller design process with guaranteed error bounds on their output trajectories. To this end, we first provide probabilistic closeness guarantees between the interconnection of stochastic switched subsystems and that of their finite abstractions via stochastic simulation functions. We then leverage sufficient small-gain type conditions to show compositionality results of this work. Afterwards, we show that under standard assumptions ensuring incremental input-to-state stability of switched systems (i.e., existence of common incremental Lyapunov functions, or multiple incremental Lyapunov functions with dwell-time), one can construct finite MDPs for the general setting of nonlinear stochastic switched systems. We also propose an approach to construct finite MDPs together with their corresponding stochastic simulation functions for a particular class of nonlinear stochastic switched systems. We show that for this class of systems, the aforementioned incremental stability property can be readily checked by matrix inequalities. To demonstrate the effectiveness of our proposed results, we first apply our approaches to a road traffic network in a circular cascade ring composed of 200 cells, and construct compositionally a finite MDP of the network. We employ the constructed finite abstractions as substitutes to compositionally synthesize policies keeping the density of the traffic lower than 20 vehicles per cell. We then apply our proposed techniques to a fully interconnected network of 500 nonlinear subsystems (totally 1000 dimensions), and construct their finite MDPs with guaranteed error bounds. We compare our proposed results with those available in the literature.

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Probabilistic simulations for probabilistic processes

Cited by 204 publications

References 18 publications

Probabilities in Session Types

Probabilities in Session Types

Computing Branching Distances Using Quantitative Games

Compositional abstraction-based synthesis for networks of stochastic switched systems

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