Capturing conflict and confusion in CSP

• Authors: Christie Marrne Bolton
• Venue: IFM'07 Proceedings of the 6th international conference on Integrated formal methods
• Year: 2007

Traditionally, developers of concurrent systems have adopted two distinct approaches: those with truly concurrent semantics and those with interleaving semantics. In the coarser interleaving interpretation parallelism can be captured in terms of non-determinism whereas in the finer, truly concurrent interpretation it cannot. Thus processes a ||b and a.b+b.a are identified within the interleaving approach but distinguished within the truly concurrent approach. In [5] we explored the truly concurrent notions of conflict, whereby transitions can occur individually but not together from a given state, and confusion, whereby the conflict set of a given transition is altered by the occurrence of another transition with which it does not interfere. We presented a translation from the truly concurrent formalism of Petri nets to the interleaving process algebra CSP and demonstrated how the CSP model-checker FDR can be used to detect the presence of both conflict and confusion in Petri nets. This work is of interest firstly because, to the author's knowledge, no existing tool for Petri nets can perform these checks, and secondly (and perhaps more significantly) because we bridged the gap between truly concurrent and interleaving formalisms, demonstrating that true concurrency can be captured in what is typically considered to be an interleaving language. In this paper we build on the work presented in [5] further embedding the truly concurrent notions of conflict and confusion in the interleaving formalism CSP by extending the domain of our translation from the simplistic subset of safe Petri nets, in which each place can hold at most one token, to standard Petri nets, in which the number of tokens in each place is unbounded.