Weak Concurrent Kleene Algebra with Application to Algebraic Verification

TL;DR

This paper extends concurrent Kleene algebra to include probabilistic effects, providing a sound algebraic framework for modeling and verifying concurrent systems with probabilistic behaviors.

Contribution

It introduces a generalized algebra that accounts for probabilistic effects in concurrency and proves its soundness with respect to automata models.

Findings

Algebraic treatment of probabilistic concurrent systems

Soundness established for the generalized algebra

Application to may testing and choice coordination problem

Abstract

We propose a generalisation of concurrent Kleene algebra \cite{Hoa09} that can take account of probabilistic effects in the presence of concurrency. The algebra is proved sound with respect to a model of automata modulo a variant of rooted $\eta$-simulation equivalence. Applicability is demonstrated by algebraic treatments of two examples: algebraic may testing and Rabin's solution to the choice coordination problem.