An Elimination Theorem for Regular Behaviours with Integration

This chapter deals with an extension of the process algebra ACP with rational time and integration. We determine a proper subdomain of the regular processes for which an elimination theorem holds, namely, for each pair of processes p0 ; p1 in this class there is a process q in this class such that p0kp1 and q are bisimilar. Some simple examples show that if this subdomain is enlarged, then the elimination result is lost. The subdomain is equivalent to the model of timed automata from Alur and Dill. 1 Introduction In recent years, process algebras such as CCS, CSP and ACP, have been extended with constructs that mean to describe some notion of either discrete or dense time. This chapter is based on the approach of Baeten and Bergstra [3], which extends ACP with real time. They introduced the notion of integration, which expresses the possibility that an action occurs somewhere within a time interval. The construct R v2V p executes the process p, where the behaviour of p may depend on..