On the Expressive Power of Restriction and Priorities in CCS with Replication

Abstract

Abstract. We study the expressive power of restriction and its interplay with replication. We do this by considering several syntactic variants of CCS ! (CCS with replication instead of recursion) which differ from each other in the use of restriction with respect to replication. We consider three syntactic variations of CCS ! which do not allow the use of an unbounded number of restrictions: CCS

Language representability of finite place/transition Petri nets

“…In particular, already in that paper it is observed that finite-net π -calculus processes originate finite P/T net systems (with inhibitor arcs). Similar observations on the interplay between parallel composition and restriction in recursive definitions, in different contexts, has been done also by others, e.g., [1]. Also important is the work of Meyer [23,24] in providing an unlabeled P/T net semantics for a fragment of the π -calculus; the main difference is that his semantics may offer a finite net representation also for some processes where restriction occurs inside recursion, but the price to pay is that the resulting net semantics may be incorrect from a causality point of view; for instance, in process (νc)(a.c.0 | b.c.0) | (ā.0 |b.0) the two synchronizations on a and b are causally dependent in his semantics.…”

“…If TS 1 = TS 2 we say that R is a bisimulation on TS 1 . Two states q and q are bisimilar, q ∼ q , if there exists a bisimulation R such that (q, q ) ∈ R.…”

“…The inductive hypothesis on the premise of rule (S-Res) ensures that there exist a transition t = (m, σ, m ) and a process p 1 …”

“…However, if we want to be more generous and consider Petri nets labeled over the set Act = L ∪ L ∪ {τ } of structured actions and co-actions, the extension of the representability theorem to this larger class of nets is not trivial. First of all, we note that the translation in Definition 17 is no longer accurate; consider the Petri net N ({s 1 …”

“…B Roberto Gorrieri roberto.gorrieri@unibo.it 1 Dipartimento di Informatica, Scienza e Ingegneria, Università di Bologna, Mura A. Zamboni, 7, 40127 Bologna, Italy Hence, this famous result of Milner offers a process calculus to represent, up to isomorphism, all and only finite-state LTSs.…”