A Unifying Approach to Decide Relations for Timed Automata and their Game Characterization

TL;DR

This paper introduces a unified, zone-based method for deciding various relations between timed automata states, avoiding explicit product constructions and providing a game-based characterization that reveals a hierarchy of timed relations.

Contribution

It presents a generic zone-based approach for deciding multiple timed relations and introduces a game characterization that reflects their hierarchy, enabling new relation definitions.

Findings

Zone-based method avoids explicit product construction

Game hierarchy reflects relation hierarchy

Distinguishing formulae can be generated for non-bisimilar states

Abstract

In this paper we present a unifying approach for deciding various bisimulations, simulation equivalences and preorders between two timed automata states. We propose a zone based method for deciding these relations in which we eliminate an explicit product construction of the region graphs or the zone graphs as in the classical methods. Our method is also generic and can be used to decide several timed relations. We also present a game characterization for these timed relations and show that the game hierarchy reflects the hierarchy of the timed relations. One can obtain an infinite game hierarchy and thus the game characterization further indicates the possibility of defining new timed relations which have not been studied yet. The game characterization also helps us to come up with a formula which encodes the separation between two states that are not timed bisimilar. Such distinguishing formulae can also be generated for many relations other than timed bisimilarity.