Split and ST Bisimulation Semantics

In this paper the notion of action atomicity is relaxed by permitting actions to be observed in the middle of their evolution. Non atomic semantic equivalences, based on the notion of bisimulation, are studied over stable event structures. Splitn bisimulation equivalence (denoted n ) considers each event as composed of n phases. ST bisimulation equivalence (denoted ST ) is a slight refinement of 2 where each ending phase is unambiguously associated to a beginning phase. We prove that, by increasing n, we get finer and finer equivalences (i.e. n+1 n ) and, moreover, that n+1 coincides with ST over those event structures whose autoconcurrency is at most n. The main consequence of these results is that, for image finite event structures, ST is the intersection of all the n . This paper will appear in Information and Computation. 1. The first author has been partially supported by the Italian CNR, grant n. 92.00069.CT12.115.25585, and the second author by Progetto Finalizzato “Calcolo Parallelo e Informatica” (obiettivo LAMBRUSCO) and Hewlett Packard Pisa Science Centre. 2. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, I-40127 Bologna, Italy. E-mail: [email protected] 3. Dipartimentodi Informatica –Università di Pisa,Corso Italia 40, I-56125,Pisa, Italy. E-mail: [email protected]