Structural operational semantics for non-deterministic processes with quantitative aspects

TL;DR

This paper introduces a general GSOS specification format called WF-GSOS for non-deterministic processes with quantitative aspects, unifying various models and proving bisimulation properties as congruences.

Contribution

It presents a unified specification format and a coalgebraic characterization for non-deterministic quantitative processes, covering many existing systems.

Findings

WF-GSOS covers models like PEPA, TIPP, PCSP.

Bisimulation is proven to be a congruence.

Soundness and completeness of the format are established.

Abstract

General frameworks have been recently 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 GSOS (WF-GSOS), 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 and completeness of the WF-GSOS specification format, and that bisimilarities induced by these specifications are always congruences.