Timed Circus: Timed CSP with the Miracle

Abstract

Abstract-Timed Circus is a compact extension to Circus; that is, it inherits only the CSP part of Circus while introducing time. Although it looks much like timed CSP from the viewpoint of syntax, its semantics is very different from that of timed CSP because it uses a complete lattice in the implication ordering instead of the complete partial order of the standard failures-divergences model of CSP. The complete lattice gives rise to a number of strange processes which violate some axioms of CSP, especially when the miracle (the top element) and SKIP meet time. In this paper, compared with timed CSP, we will extensively explore such strange processes which turn out to be very useful in specifying a distinct property that 'something must occur'. Finally, we use a simple example to demonstrate how our model can contribute to modelling temporal behaviours with multiple time scales in complex systems.

RoboChart: modelling and verification of the functional behaviour of robotic applications

“…4 as a basis to define a timed semantics for RoboChart. As previously stated, our formalisation targets the UTP, but we use CSP as a front end and, in particular, for modelling time, we use discrete Timed CSP [88] enriched with a notion of deadlines [98]. For the purpose of early validation using FDR, we encode this Timed CSP semantics into a dialect of CSP, namely, tock-CSP, as described later in Sect.…”

“…We consider, however, a discrete-time semantics for these operators. It is given in the context of Circus Time [91,98], a timed process algebra based on CSP, and, therefore, Timed CSP, but with a UTP discrete-time model. In our tock-CSP encoding, we define all these operators as well (see Sect.…”

Angelic processes for CSP via the UTP

“…We consider an angelic choice between termination and deadlock. Although the miraculous process ⊤ R is not part of the standard CSP semantics [2] it plays an important role, for example, in the characterisation of deadline operators in the context of timed versions of process calculi [37,38,39].…”