Timed process calculi with deterministic or stochastic delays: Commuting between durational and durationless actions

Abstract

Several deterministically/stochastically timed process calculi have been proposed in the literature that, apart from their synchronization mechanism, mainly differ for the way in which actions and delays are represented. In particular, a distinction is made between integrated-time calculi, in which actions are durational, and orthogonal-time calculi, in which actions are instantaneous and delays are expressed separately. In a previous work on deterministic time, the two approaches have been shown to be reconcilable through an encoding from the integrated-time calculus CIPA to the orthogonal-time calculus TCCS, which preserves strong timed bisimilarity under certain conditions. In this paper, the picture is completed by first defining a reverse encoding from TCCS to CIPA, which requires slight modifications to both calculi and is shown to preserve only weak timed bisimilarity under conditions tighter than those for the direct encoding. Stochastic time is then addressed, by exhibiting an encoding from the integrated-time calculus MTIPP to the orthogonal-time calculus IML, together with a reverse encoding requiring slight modifications only to the former calculus, with both encodings being shown to preserve strong Markovian bisimilarity under suitable conditions. All the four encodings rely on the assumption that action execution is urgent. Variants are finally discussed in which action execution is delayable, in the sense that an enabled action can let time advance before starting its execution, or only the execution of internal actions is urgent, which is known as maximal progress

The Reversible Temporal Process Language

“…This resembles maximal progress for the timeout operator. A deep comparison between deterministic time, used by TPL, and stochastic time used by stochastic process algebras can be found in [1]. Further investigation on the relation between our work and [2], studying reversibility in Markov chains, is left for future work.…”

“…In the last years several reversible semantics for concurrency have been developed, see, e.g., [8,7,18,2,22]. However, none of them takes into account time 1 . Time-dependent behaviour is an intrinsic and important feature of real-world concurrent systems and has many applications: from the engineering of highways [21], to the manufacturing schedule [11] and to the scheduling problem for real-time operating systems [3].…”

revTPL: The Reversible Temporal Process Language

“…This is similar to maximal progress for the timeout operator. A deep comparison between deterministic time, used by TPL, and stochastic time, used by stochastic process algebras, can be found in [BCT16]. Further investigation on the relation between our work and [BM20], studying reversibility in Markov chains, is left for future work.…”

“…The application of our approach using integrated semantics and/or absolute time should not present any particular challenge. In fact, separated and integrated semantics have been shown to be equivalent [BCT16] (i.e., they can be encoded into each other preserving weak barbed bisimilarity). Similarly for absolute instead of relative time thanks to the equivalence given in [Cor00].…”

“…It may require us to record some live information on the different time perspective of parallel processes to rule out unwanted interleavings. An alternative could be to exploit the encoding of [BCT16] from TCCS to CIPA, and see whether the semantics is still preserved while considering reversible behaviours.…”