The Theory of Traces for Systems with Nondeterminism, Probability, and Termination

TL;DR

This paper develops a coalgebraic framework for trace semantics in systems with nondeterminism, probability, and termination, providing a unified approach and comparing it to existing trace equivalences.

Contribution

It introduces a coalgebraic trace semantics using the generalized powerset construction for complex systems combining nondeterminism and probability.

Findings

Trace semantics can be derived via a coalgebraic approach.

The framework unifies and compares existing trace equivalences.

Results highlight the role of monads and algebraic theories in system semantics.

Abstract

This paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics for such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. We characterise and compare the resulting semantics to known definitions of trace equivalences appearing in the literature. Most of our results are based on the exciting interplay between monads and their presentations via algebraic theories.