Abstract
Specifying budgets and deadlines using a process algebra like CSP requires an explicit notion of time. The tock-CSP encoding embeds a rich and flexible approach for modelling discrete-time behaviours with powerful tool support. It uses an event tock, interpreted to mark passage of time. Analysis, however, has traditionally used the standard semantics of CSP, which is inadequate for reasoning about timed refinement. The most recent version of the model checker FDR provides tailored support for tock-CSP, including specific operators, but the standard semantics remains inadequate. In this paper, we characterise tock-CSP as a language in its own right, rich enough to model budgets and deadlines, and reason about Zeno behaviour. We present the first sound tailored semantic model for tock-CSP that captures timewise refinement. It is fully mechanised in Isabelle/HOL and, to enable use of FDR4 to check refinement in this novel model, we use model shifting, which is a technique that explicitly encodes refusals in traces.
Highlights
In the realm of cyber-physical systems, time is a crucial concern
The first two rows indicate whether a semantic model captures termination, deadlines, and Zeno behaviour: only failures [38], refusal testing [28,34], discrete-time refusal traces [32] and -tock provide full support, satisfying Property 2
For validation of our definitions, we prove that the set of traces of all processes defined using our operators satisfy the healthiness conditions described in Sect
Summary
In the realm of cyber-physical systems, time is a crucial concern. Such reactive systems can be modelled as cooperating with their environment via named events that correspond to atomic and instantaneous interactions of interest over their lifetime. Roscoe [37] has proposed tock-CSP, where the event tock encodes the passage of discrete time, allowing existing CSP tools like FDR to be used for reasoning about timed models. The most recent version of FDR offers a syntactic environment called a timed section that translates untimed processes into tock-CSP, to facilitate the specification of timed models, reusing the syntax of standard CSP and interpreting the operators in the context of a (discrete) timed semantics. Our contribution is a novel semantic model for tock-CSP that allows the specification of deadlines, that caters for termination and Zeno behaviour, and whose refinement relation is timewise refinement. The model and operators are specified in Isabelle/HOL [30] Another contribution is an environment for mechanical theorem proving that paves the ground for the development of refinement tools for tock-CSP.
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