GSOS for non-deterministic processes with quantitative aspects

TL;DR

This paper introduces a general GSOS format called WFSOS for specifying non-deterministic processes with quantitative aspects, unifying various models and proving bisimulation congruence through coalgebraic characterization.

Contribution

It presents a new WFSOS specification format for non-deterministic quantitative processes and characterizes these systems as coalgebras, ensuring soundness and congruence of bisimulations.

Findings

WFSOS covers many known systems like PEPA, TIPP, PCSP.

Bisimulations are always congruences under WFSOS.

Coalgebraic characterization proves soundness of the format.

Abstract

Recently, some general frameworks have been proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools. This paper provides two contributions in this respect. First, we present a general GSOS specification format (and a corresponding notion of bisimulation) for non-deterministic processes with quantitative aspects. These specifications define labelled transition systems according to the ULTraS model, an extension of the usual LTSs where the transition relation associates any source state and transition label with state reachability weight functions (like, e.g., probability distributions). This format, hence called Weight Function SOS (WFSOS), covers many known systems and their bisimulations (e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS, Segala-GSOS, among others). The second contribution is a characterization of these systems as coalgebras of a class of functors, parametric on the weight structure. This result allows us to prove soundness of the WFSOS specification format, and that bisimilarities induced by these specifications are always congruences.