3 research outputs found
Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets
We propose a framework for the specification of behaviour-preserving
reconfigurations of systems modelled as Petri nets. The framework is based on
open nets, a mild generalisation of ordinary Place/Transition nets suited to
model open systems which might interact with the surrounding environment and
endowed with a colimit-based composition operation. We show that natural
notions of bisimilarity over open nets are congruences with respect to the
composition operation. The considered behavioural equivalences differ for the
choice of the observations, which can be single firings or parallel steps.
Additionally, we consider weak forms of such equivalences, arising in the
presence of unobservable actions. We also provide an up-to technique for
facilitating bisimilarity proofs. The theory is used to identify suitable
classes of reconfiguration rules (in the double-pushout approach to rewriting)
whose application preserves the observational semantics of the net.Comment: To appear in "Logical Methods in Computer Science", 41 page
Connector algebras for C/E and P/T nets interactions
A quite fourishing research thread in the recent literature on component based system is concerned with the algebraic properties of different classes of connectors. In a recent paper, an algebra of stateless connectors was presented that consists of five kinds of basic connectors, namely symmetry, synchronization, mutual exclusion, hiding and inaction, plus their duals and it was shown how they can be freely composed in series and in parallel to model sophisticated "glues". In this paper we explore the expressiveness of stateful connectors obtained by adding one-place buffers or unbounded buffers to the stateless connectors. The main results are: i) we show how different classes of connectors exactly correspond to suitable classes of Petri nets equipped with compositional interfaces, called nets with boundaries; ii) we show that the difference between strong and weak semantics in stateful connectors is reflected in the semantics of nets with boundaries by moving from the classic step semantics (strong case) to a novel banking semantics (weak case), where a step can be executed by taking some "debit" tokens to be given back during the same step; iii) we show that the corresponding bisimilarities are congruences (w.r.t. composition of connectors in series and in parallel); iv) we show that suitable monoidality laws, like those arising when representing stateful connectors in the tile model, can nicely capture concurrency aspects; and v) as a side result, we provide a basic algebra, with a finite set of symbols, out of which we can compose all P/T nets, fulfilling a long standing quest