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

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.