The Measurable Space of Stochastic Processes

Issue title: Formal Models - Computability, Complexity, Applications

Article type: Research Article

Authors: Cardelli, Luca | Mardare, Radu

Affiliations: Microsoft Research Cambridge, UK. [email protected] | Dept. of Computer Science, Aalborg University, Denmark. [email protected]

Note: [] Address for correspondence: Microsoft Research Cambridge, UK

Abstract: 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.

Keywords: Markov processes, stochastic process algebras, structural operational semantics

DOI: 10.3233/FI-2014-1019

Journal: Fundamenta Informaticae, vol. 131, no. 3-4, pp. 351-371, 2014