Structural Operational Semantics for Continuous State Probabilistic Processes

Bacci, Giorgio; Miculan, Marino

doi:10.1007/978-3-642-32784-1_5

Cited by 8 publications

(6 citation statements)

References 30 publications

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“…Remark 1 (Expressing interpretations). The definition of a weight term interpretation can be done in many ways, such as structural recursion or λ -iteration [1]. For instance, every family of maps:…”

Section: Wfsos: a Gsos Format For Ultrassmentioning

confidence: 99%

“…This syntax can be thought as an "intermediate language" for representing weight functions along the line of viewing ULTraSs as stratified (or staged) systems. An early example of this approach can be found in [1], where targets are terms representing measures over the continuous state space. Earlier steps in this direction can be found e.g.…”

Section: Wfsos: a Gsos Format For Ultrassmentioning

confidence: 99%

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GSOS for non-deterministic processes with quantitative aspects

Miculan

Peressotti

2014

Electron. Proc. Theor. Comput. Sci.

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Recently, some general frameworks have been proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools. This paper provides two contributions in this respect. First, we present a general GSOS specification format (and a corresponding notion of bisimulation) for non-deterministic processes with quantitative aspects. These specifications define labelled transition systems according to the ULTraS model, an extension of the usual LTSs where the transition relation associates any source state and transition label with state reachability weight functions (like, e.g., probability distributions). This format, hence called Weight Function SOS (WFSOS), covers many known systems and their bisimulations (e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS, Segala-GSOS, among others). The second contribution is a characterization of these systems as coalgebras of a class of functors, parametric on the weight structure. This result allows us to prove soundness of the WFSOS specification format, and that bisimilarities induced by these specifications are always congruences.Comment: In Proceedings QAPL 2014, arXiv:1406.156

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Section: Wfsos: a Gsos Format For Ultrassmentioning

confidence: 99%

Section: Wfsos: a Gsos Format For Ultrassmentioning

confidence: 99%

GSOS for non-deterministic processes with quantitative aspects

Miculan

Peressotti

2014

Electron. Proc. Theor. Comput. Sci.

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“…Using a non-discrete σalgebra makes our approach different, while considering the measurable sets closed to some congruence relation makes it more appropriate for modelling and for extensions to other equational theories. Recent papers followed and generalized the ideas proposed in this paper [4,5].…”

Section: Related Workmentioning

confidence: 92%

The Measurable Space of Stochastic Processes

Cardelli

Mardare

2014

Fundamenta Informaticae

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We introduce a stochastic extension of CCS endowed with structural operational semantics expressed in terms of measure theory. The set of processes is organised as a measurable space by the sigma-algebra generated by structural congruence. The structural operational semantics associates to each process a set of measures over the space of processes. The measures encode the rates of the transitions from a process (state of a system) to a measurable set of processes. We prove that the stochastic bisimilarity is a congruence, which extends the structural congruence. In addition to an elegant operational semantics, our calculus provides a canonic way to define metrics on processes that measure how similar two processes are in terms of behaviour. This paper treats a similar subject looking into the algebraic foundations of stochastic process algebras that are nowadays used to model complex real systems. This paper is a revised version of [12]. At the time of its first publication, this paper opened a new research direction revealing the necessity to involve measure theory into the research on structural operational semantics.Process algebras (PAs) [7] are formalisms designed to describe the evolution of concurrent communicating systems. For capturing observable behaviors, PAs are conceptualised along two orthogonal axes. From an algebraic point of view, they are endowed with construction principles in the form of algebraic operations that allow composing larger processes from more basic ones; a process is identified by its algebraic term. On the other hand, there exists a notion of nondeterministic evolution, described by a coalgebraic structure, in the form of a transition system. The algebraic and coalgebraic structures are not independent: Structural Operational Semantics (SOS) defines the behavior of a process inductively on its syntactic structure. In this way, classic PAs are supported by an easy and appealing underlying theory that guarantees their success.In the past decades probabilistic and stochastic behaviors have also become of central interest due to the applications in performance evaluation and computational systems biology. Stochastic process algebras such as TIPP [23], PEPA [26,27], EMPA [8] and stochastic π-calculus [37] have been defined as extensions of classic PAs, by considering more complex coalgebraic structures. The label of a stochastic transition contains, in addition to the name of the action, the rate of an exponentially distributed random variable that characterizes the duration of the transition. Consequently, SOS associates a non-negative rate value to each tuple state, action, state . This additional information imposes important modifications in the SOS format, such as the multi-transition system approach of PEPA or the proved SOS approach of stochastic π-calculus, mainly because the nondeterminism is replaced by the race policy.With the intention of developing a stochastic process calculus for applications in systems biology, in this paper we propose a stochastic version of CCS [34] ...

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“…He developed the SGSOS format to define wellbehaved Markovian stochastic transition systems [18]. A closely related approach was taken by Bacci and Miculan for probabilistic processes with continuous probabilities [3]. It is worth investigating how our modal decomposition approach relates to bialgebraic methods.…”

Section: Future Workmentioning

confidence: 99%

Compositionality of Probabilistic Hennessy-Milner Logic through Structural Operational Semantics

Gebler¹,

Fokkink

2012

Lecture Notes in Computer Science

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Abstract. We present a method to decompose HML formulae for reactive probabilistic processes. This gives rise to a compositional modal proof system for the satisfaction relation of probabilistic process algebras. The satisfaction problem of a probabilistic HML formula for a process term is reduced to the question of whether its subterms satisfy a derived formula obtained via the operational semantics.

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Structural Operational Semantics for Continuous State Probabilistic Processes

Cited by 8 publications

References 30 publications

GSOS for non-deterministic processes with quantitative aspects

GSOS for non-deterministic processes with quantitative aspects

The Measurable Space of Stochastic Processes

Compositionality of Probabilistic Hennessy-Milner Logic through Structural Operational Semantics

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