Approximate Testing Equivalence Based on Time, Probability, and Observed Behavior

TL;DR

This paper introduces a new approximate testing equivalence framework for process models, incorporating execution time, event probability, and observed behavior to enable flexible comparison and verification.

Contribution

It proposes a novel approach to approximate testing equivalence that considers multiple orthogonal aspects, enhancing flexibility and applicability in process comparison.

Findings

Framework unifies time, probability, and behavior in testing equivalence

Discusses interpretation and decidability of verification algorithms

Enables flexible comparison of non-behaviorally equivalent models

Abstract

Several application domains require formal but flexible approaches to the comparison problem. Different process models that cannot be related by behavioral equivalences should be compared via a quantitative notion of similarity, which is usually achieved through approximation of some equivalence. While in the literature the classical equivalence subject to approximation is bisimulation, in this paper we propose a novel approach based on testing equivalence. As a step towards flexibility and usability, we study different relaxations taking into account orthogonal aspects of the process observations: execution time, event probability, and observed behavior. In this unifying framework, both interpretation of the measures and decidability of the verification algorithms are discussed.