Differential Bisimulation for a Markovian Process Algebra

Iacobelli, Giulio; Tribastone, Mirco; Vandin, Andrea

doi:10.1007/978-3-662-48057-1_23

Cited by 16 publications

(17 citation statements)

References 20 publications

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“…Lastly we consider a fragment of Fluid Process Algebra (FPA) presented in [49], which corresponds to the process algebra studied in [77]. The grammar of FPA considers parallel composition of sequential processes with synchronization over shared actions.…”

Section: Process Algebramentioning

confidence: 99%

“…We refer the reader to the literature (e.g., [49,77]) for a more detailed discussion on the semantics of FPA. Here we stress that the crucial definition is r * α (M1 L M2) for a synchronization action α ∈ L. Intuitively, it provides a contribution to the drift that establishes a threshold-based contention between the capacities (i.e., rates) of the operands, dictated by the minimum function.…”

Section: Process Algebramentioning

confidence: 99%

“…The first equivalence for FPA that we study is differential bisimulation [49]. It is a relation over the set of constants of an FPA model, defined in terms of conditions on the sequential behavior and on the compositional structure of processes.…”

Section: Differential Bisimulationmentioning

confidence: 99%

“…We discuss why it is not a necessary condition using the example taken from [49]. It can be shown that ZF = {{P1}, {P2, P3}, {Q1}, {Q2}} is a differential bisimulation, hence the corresponding partition on the IDOL variables HF = {{xP 1 }, {xP 2 , xP 3 }, {xQ 1 }, {xQ 2 }} is an FDE.…”

Section: Differential Bisimulationmentioning

confidence: 99%

“…We take PEPA as the representative of a family of languages for the quantitative evaluation of computing systems -indeed it is expressive enough to cover the semantics of a popular class of queuing networks [75] and Petri nets [39]. We show that recently proposed behavioral equivalences for PEPA [49,77] are special, language-specific cases of our differential equivalences.…”

Section: Introductionmentioning

confidence: 99%

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Symbolic computation of differential equivalences

et al. 2016

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Ordinary differential equations (ODEs) are widespread in many natural sciences including chemistry, ecology, and systems biology, and in disciplines such as control theory and electrical engineering. Building on the celebrated molecules-as-processes paradigm, they have become increasingly popular in computer science, with high-level languages and formal methods such as Petri nets, process algebra, and rule-based systems that are interpreted as ODEs. We consider the problem of comparing and minimizing ODEs automatically. Influenced by traditional approaches in the theory of programming, we propose differential equivalence relations. We study them for a basic intermediate language, for which we have decidability results, that can be targeted by a class of high-level specifications. An ODE implicitly represents an uncountable state space, hence reasoning techniques cannot be borrowed from established domains such as probabilistic programs with finite-state Markov chain semantics. We provide novel symbolic procedures to check an equivalence and compute the largest one via partition refinement algorithms that use satisfiability modulo theories. We illustrate the generality of our framework by showing that differential equivalences include (i) well-known notions for the minimization of continuous-time Markov chains (lumpability), (ii)~bisimulations for chemical reaction networks recently proposed by Cardelli et al., and (iii) behavioral relations for process algebra with ODE semantics. With a prototype implementation we are able to detect equivalences in biochemical models from the literature that cannot be reduced using competing automatic techniques.

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Section: Process Algebramentioning

confidence: 99%

Section: Process Algebramentioning

confidence: 99%

Section: Differential Bisimulationmentioning

confidence: 99%

Section: Differential Bisimulationmentioning

confidence: 99%