From Causal Semantics To Duration Timed Models

TL;DR

This paper develops a framework combining causality and dense time semantics by extending causal transition systems and CSP with durations, enabling more accurate modeling of durational actions in concurrent systems.

Contribution

It introduces a real-time extension of CSP called duration-CSP with a formal semantics, and proves the preservation of bisimulation under action refinement.

Findings

Extended causal transition systems with clocks and constraints.

Defined and proved equivalence of operational and denotational semantics for duration-CSP.

Extended duration-CSP with a refinement operator that preserves bisimulation.

Abstract

The interleaving semantics is not compatible with both action refinement and durational actions. Since many true concurrency semantics are congruent w.r.t. action refinement, notably the causality and the maximality ones, this has challenged us to study the dense time behavior - where the actions are of arbitrary fixed duration - within the causality semantics of Da Costa. We extend the causal transition systems with the clocks and the timed constraints, and thus we obtain an over class of timed automata where the actions need not to be atomic. We define a real time extension of the formal description technique CSP, called duration-CSP, by attributing the duration to actions. We give the operational timed causal semantics of duration-CSP as well as its denotational semantics over the class of timed causal transition systems. Afterwards, we prove that the two semantics are equivalent. Finally we extend the duration-CSP language with a refinement operator $\rho$ - that allows to replace an action with a process - and prove that it preserves the timed causal bisimulation.