Structural Operational Semantics for Stochastic Process Calculi

Abstract

A syntactic framework called SGSOS, for defining well-behaved Markovian stochastic transition systems, is introduced by analogy to the GSOS congruence format for nondeterministic processes. Stochastic bisimilarity is guaranteed a congruence for systems defined by SGSOS rules. Associativity of parallel composition in stochastic process algebras is also studied within the framework.

The How and Why of Interactive Markov Chains

“…In IMC, the separation of delays and actions allows to treat action synchronisation as in standard concurrency models. It is surprising that given the advantages of IMCs, recent approaches for CTMC-variants of process calculi for mobility and service-oriented computing [59] and interesting new developments in structured operational semantics for such calculi [50,24] do not adopt this approach.…”

Stochastic Pi-calculus Revisited

“…It provides simple solutions to the problems of replications and bound outputs which otherwise, as with Milner's Abstraction-Concretion method [18], require complicated high-order reasoning. Also novel is our concept of stochastic bisimulation that extends other similar ones [17,15,6,19] by making explicit the role of the rate environments. We show that bisimulation is a congruence that extends the structural congruence.…”

“…These result in complex constructs that are difficult to extend to a general format for well-behaved stochastic specifications and problematic when recursion or fresh name quantification are considered. As underlined in [15], for stochastic pi-calculus of [20] the parallel composition fails to be associative up to bisimulation, while for PEPA, if arbitrary relations between the rates of processes and subprocesses are allowed, stochastic bisimulation ceases to be a congruence. An explanation for these situations is given in [15]: the information carried by the aforementioned SOS frameworks is excessive, while a well-behaved framework should only carry the exact amount of data required for the derivation of the intended semantics.…”

“…The transition-systems-as-coalgebras paradigm [8,21] exploits it providing a uniform characterisation of transition systems that covers the sequence nondeterministic, probabilistic and stochastic systems. Similar approaches have been tested with SPAs in [7] and a general SOS format for SPAs without new name operators or recursion is proposed in [15]; these approaches consider the space of processes organized by powerset. Instead, we take a different measurable space that answers to practical modelling requirements, simplifies the semantics and gives us smooth solutions for the fresh name quantification and replication without requiring additional constructs.…”

Structural Operational Semantics for Continuous State Probabilistic Processes

“…Bartels [6] and Klin and Sassone [20] have investigated rule formats (called Probabilistic GSOS and Stochastic GSOS, respectively) which guarantee bisimilarity to be a congruence.…”