The Measurable Space of Stochastic Processes

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 stochastic bisimulation is a congruence that extends structural congruence. In addition to an elegant operational semantics, our calculus provides a canonic way to define metrics on processes that measure that measure how similar two processes are in terms of behaviour. Keywords-Markov processes, stochastic process algebras, structural operational semantics

• Type: Journal
• Year: 2010
• Where: QEST
• Authors: Luca Cardelli, Radu Mardare
• Keywords: Modeling And Simulation, Operational Semantics, QEST 2010, Structural Congruence, Structural Operational Semantics