Global Timed Bisimulation: An Introduction

Abstract

Bisimulations are a broadly used formalism to define the semantics of process algebras. In particular, by means of weak bisimulation most of the internal activity of processes may be abstracted. Unfortunately, this is not fully accomplished: for instance, the internal choice operator becomes non-associative since bisimulation can see the branching structure of processes. In this paper we propose global timed bisimulation as a weakening of weak timed bisimulation. Global timed bisimulation is defined exactly as weak timed bisimulation once ordinary transitions are replaced by the adequate notions of generalized transitions. In order to asses the definition of our global timed bisimulation we present a collection of small examples that illustrate each of the clauses of that definition. Finally, a more elaborated example is presented to summarize the main properties of that notion.

A Global Timed Bisimulation Preserving Abstraction for Parametric Time-Interval Automata

“…In particular, branch restructuring plays an important role in the optimization. It is true that timed weak bisimulation was proposed to determine equivalence of processes considering both time and observability [10], but as pointed out by [2], timed weak bisimulation may not be suitable for equivalence checking of real time software in the presence of optimization via branch restructuring. Therefore we employ GTB to determine equivalence of processes, since GTB is a weakening of timed weak bisimulation in that internal branch structures are ignored.…”

“…[2], as well as the definition of the traditional timed weak bisimulation [11,10] (TWB) and its relation to the GTB.…”

“…Global timed bisimulation [2] is a variant of bisimulation equivalence which consider both timing and observability. Unlike timed weak bisimulation, global timed bisimulation does not distinguish the difference of branching structures of internal transitions.…”

“…Firstly, in order to make it suitable for our formalism, we rephrase the definition of a static generalized transition relation −→ gt and a dynamic generalized transition relation α −→ gt , which are proposed in Ref. [2]. The intention of the following definition is that, from the original timed LTS, we want to construct a new timed LTS using −→ gt and α −→ gt such that the constructed LTS contains many other possible branching structures derived from the original one, which is practically indistinguishable by any external observer (that is, any realistic tester).…”

“…It has only a time interval with upper-and lower-bound parameters as a relative timing constraint between consecutive actions. In this paper, at first, we propose an abstraction algorithm of PTIA which preserves global timed bisimulation [2]. Global timed bisimulation is weaker than timed weak bisimulation and a sufficient condition for timed testing equivalence.…”