Nadia Busi

A Petri Net Semantics for pi-Calculus

A distributed semantics for π-calculus, based on P/T Petri nets with inhibitor arcs, is presented. This net semantics is sound w.r.t. the original early transition system semantics: the interleaving semantics of an agent p is retrievable from the net by considering the interleaving marking graph for the associated marking dec(p). Furthermore, π-calculus is equipped with a multistep and a causal semantics. The latter is compared with recent proposals appeared in the literature.

Non Sequential Semantics for Contextual P/T Nets

The problem of finding a true concurrent semantics for contextual P/T nets has not been deeply studied yet. The interest for such a semantics has been renewed by some recent proposals to equip mobile process algebras with a net semantics based on this model. In [3] we proposed a causal semantics for such nets, in this paper we study the non sequential semantics of contextual P/T nets. The semantics is based on a suitable notion of occurrence net and, equipped with a notion of history preserving bisimulation, is more discriminating of the contextual one in general, whereas both are equivalent if we restrict our attention to positive context only.

Synthesis of Nets with Inhibitor Arcs

The synthesis problem for Petri nets consists in the construction of a net system whose behaviour is specified by a given transition system. In this paper we deal with the synthesis of elementary net systems extended with inhibitor arcs, i.e. arcs that test for absence of tokens in a place. We characterize the class of transitions systems corresponding to the sequential execution of these nets, which is a proper extension of the one obtained by the execution of nets without inhibitor arcs. Finally, we try to minimize the number of inhibitor arcs; we look for conditions guaranteeing that an inhibitor arc is really used, i.e. its presence influences the behaviour of the net.

A Distributed Semantics for EMPA Based on Stochastic Contextual Nets

Extended Markovian Process Algebra (EMPA) is a stochastic process algebra equipped with an interleaving semantics, a Markovian semantics and a net semantics. The main drawback of its net semantics is that it usually associates huge nets with EMPA terms. Here we propose a new net semantics, based on contextual nets, in order to obtain more compact net representations for EMPA terms.

Three Semantics of the Output Operation for Generative Communication

A simple, yet Turing powerful, calculus based on generative communication is introduced; among its primitives, it contains a conditional input operation that tests for presence (or absence) of an output, reminiscent of the inp predicate of Linda. We study three different operational semantics for the output operation, called instantaneous, ordered and unordered. The associated behavioural semantics are obtained as the coarsest congruence contained in the corresponding strong barbed semantics. We prove that when the output operation is instantaneous, the obtained semantics is a sort of asynchronous bisimulation; on the contrary, for the ordered semantics, as well as for the unordered one, the resulting semantics is a small variant of the classic (synchronous) bisimulation. A further result is that the language under unordered semantics is no more Turing powerful, hence the language becomes strictly less expressive.

Distributed Conflicts in Communicating Systems

We argue that the alternative composition operator of CCS not only lacks expressiveness, but also provides a too abstract description of conflicting activities. Hence, we propose to replace it with a unary conflict operator and a conflict restriction operator, yielding the process algebra DiX. We show that DiX is a semantic extension of CCS. Moreover, DiX is equipped with a simple distributed semantics defined in terms of nets with inhibitor arcs, where the set of transitions is generated by three axiom schemata only. This net semantics is the main motivation for the present proposal.