A Unary Semigroup Trace Algebra

The Unifying Theories of Programming (UTP) of Hoare and He promote the unification of semantics catering for different concerns, such as, termination, data modelling, concurrency and time. Process calculi like Circus and CSP can be given semantics in the UTP using reactive designs whose traces can be abstractly specified using a monoid trace algebra. The prefix order over traces is defined in terms of the monoid operator. This order, however, is inadequate to characterise a broader family of timed process algebras whose traces are preordered instead. To accommodate these, we propose a unary semigroup trace algebra that is weaker than the monoid algebra. This structure satisfies some of the axioms of restriction semigroups and is a right P-Ehresmann semigroup. Reactive designs specified using it satisfy core laws that have been mechanised so far in Isabelle/UTP. More importantly, our results improve the support for unifying trace models in the UTP

Sound reasoning in tock-CSP

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

On timed models and full abstraction

In this paper we study a denotational model for a discrete-time version of CSP. We give a compositional semantics for the language. The model records refusal information at the end of each time unit; we believe this model to be simpler than existing models. We also show that the model is fully abstract: equivalence in the model corresponds to the natural equivalence of may testing; and all members of the denotational model are syntactically expressible. We also consider a slightly weaker model, containing no refusal information; we show that this model corresponds to an alternative form of may testing. We briefly discuss the application of these models to the study of information flow in multi-level secure systems.</p

On Timed Models and Full Abstraction

AbstractIn this paper we study a denotational model for a discrete-time version of CSP. We give a compositional semantics for the language. The model records refusal information at the end of each time unit; we believe this model to be simpler than existing models. We also show that the model is fully abstract: equivalence in the model corresponds to the natural equivalence of may testing; and all members of the denotational model are syntactically expressible. We also consider a slightly weaker model, containing no refusal information; we show that this model corresponds to an alternative form of may testing. We briefly discuss the application of these models to the study of information flow in multi-level secure systems