Processes Parametrised by an Algebraic Theory

TL;DR

This paper introduces a unified algebraic framework for various process calculi, providing semantics, axioms, and new calculi for probabilistic and convex processes, enhancing understanding of process equivalences.

Contribution

It develops a uniform (co)algebraic approach to process calculi, including new calculi for probabilistic and convex processes with Kleene star analogues.

Findings

Unified semantics and axioms for process calculi

Fragments capturing known calculi like regular expressions and guarded Kleene algebra

New calculi for probabilistic and convex processes

Abstract

We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic equivalence. We show that there are uniformly defined fragments of our calculi that capture well-known examples from the literature like regular expressions modulo bisimilarity and guarded Kleene algebra with tests. We also derive new calculi for probabilistic and convex processes with an analogue of Kleene star.