Time abstracted bisimulation: Implicit specifications and decidability

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In the last few years a number of real-time process calculi have emerged with the purpose of capturing important quantitative aspects of real-time systems. In addition, a number of process equivalences sensitive to time-quantities have been proposed, among these the notion of timed (bisimulation) equivalence in [RR86, DS89, HR91, BB89, NRSV90, MT90, Wan91b].

In this paper, we introduce a time-abstracting (bisimulation) equivalence, and investigate its properties with respect to the real-time process calculus of [Wan90]. Seemingly, such an equivalence would yield very little information (if any) about the timing properties of a process. However, time-abstracted reasoning about a composite process may yield important information about the relative timing-properties of the components of the system. In fact, we show as a main theorem that such implicit reasoning will reveal all timing aspects of a process. More precisely, we prove that two processes are interchangeable in any context up to time-abstracted equivalence precisely if the two processes are themselves timed equivalent.

As our second main theorem, we prove that time-abstracted equivalence is decidable for the calculus of [Wan90] using classical methods based on a finite-state symbolic, structured operational semantics.