An expressiveness study of priority in process calculi

Abstract

In memory of Nadia BusiPriority is a frequently used feature of many computational systems. In this paper we study the expressiveness of two process algebras enriched with different priority mechanisms. In particular, we consider a finite (that is, recursion-free) fragment of asynchronous CCS with global priority (FAP, for short) and Phillips' CPG (CCS with local priority), and contrast their expressive power with that of two non-prioritised calculi, namely the π-calculus and its broadcast-based version, called bπ. We prove, by means of leader-election-based separation results, that, under certain conditions, there exists no encoding of FAP in π-Calculus or CPG. Moreover, we single out another problem in distributed computing, which we call the last man standing problem (LMS for short), that better reveals the gap between the two prioritised calculi above and the two non-prioritised ones, by proving that there exists no parallel-preserving encoding of the prioritised calculi in the non-prioritised calculi retaining any sincere (complete but partially correct, that is, admitting divergence or premature termination) semantics.

A criterion for separating process calculi

“…homomorphy for parallel composition, has been used as a requirement (for the encodings) in [28,34] for separating CPG from both CCS and π-calculus, thus obtaining results similar to our Proposition 5.2. It is a requirement for the class of uniform encodings (that, other than distribution, are required to preserve renaming, i.e.…”

“…A second contribution consists in presenting a number of results coming from the application of our metatheory to well-known process calculi, that are possibly extensions of CCS or π-calculus. We thus end up to retrieve separation results similar to, e.g., [16,15], but ours are stronger since they hold for a more general class of encodings, or to, e.g., [8,28,34], but here they follow by possibly simpler proofs. Finally, some other results, e.g.…”

“…Indeed, we also show that variants of π-calculus equipped with, respectively, match among names [22], polyadic synchronization [8] or pattern matching [15] are only weakly rep-free and thus are strictly more expressive than the 'classical' π-calculus. This allows us to prove in a quite simple and uniform way possibly stronger versions of the results obtained in [28,8,16,15,34]. As concerns these calculi, strong replacement freeness is violated because a process originally invisible can be transformed into a visible one via application of a name substitution (generated by the enclosing context) which originates a new computation.…”

“…Hence, CPG is somehow more expressive than CCS. In [28,34] it is also argued that expressiveness of CPG and π-calculus is not comparable.…”

“…This is an effective approach, but there is no common agreement on which class of encodings has to be used. Several different classes have been introduced (see, e.g., [11,8,26,16,15,27,28,3,34,13]), each one being characterised by the syntactic and semantic properties that the encodings are required to satisfy. Appropriateness of a class depends however from the kind of results one is seeking.…”