Dependencies and Simultaneity in Membrane Systems

Membrane system computations proceed in a synchronous fashion: at each step all the applicable rules are actually applied. Hence each step depends on the previous one. This coarse view can be refined by looking at the dependencies among rule occurrences, by recording, for an object, which was the a rule that produced it and subsequently (in a later step), which was the a rule that consumed it. In this paper we propose a way to look also at the other main ingredient in membrane system computations, namely the simultaneity in the rule applications. This is achieved using zero-safe nets that allows to synchronize transitions, i.e., rule occurrences. Zero-safe nets can be unfolded into occurrence nets in a classical way, and to this unfolding an event structure can be associated. The capability of capturing simultaneity of zero-safe nets is transferred on the level of event structure by adding a way to express which events occur simultaneously

Relational structures for concurrent behaviours

\ua9 2020 The Author(s). Relational structures based on acyclic relations can successfully model fundamental aspects of concurrent systems behaviour. Examples include Elementary Net systems and Mazurkiewicz traces. There are however cases where more general relational structures are needed. In this paper, we present a general model of relational structures which can be used for a broad class of concurrent behaviours. We demonstrate how this general set-up works for combined order structures which are based on two relations, viz. an acyclic ‘before’ relation and a possibly cyclic ‘not later than’ relation

Classifying Invariant Structures of Step Traces

In the study of behaviours of concurrent systems, traces are sets of behaviourally equivalent action sequences. Traces can be represented by causal partial orders. Step traces, on the other hand, are sets of behaviourally equivalent step sequences, each step being a set of simultaneous actions. Step traces can be represented by relational structures comprising non-simultaneity and weak causality. In this paper, we propose a classification of step alphabets as well as the corresponding step traces and relational structures representing them. We also explain how the original trace model fits into the overall framework.Algorithms and the Foundations of Software technolog

An Event Based Semantics of P Systems

Membrane systems have many similarities with classical concurrency models. In particular notions like parallelism, causality and concurrency seem to belong to membrane computing, though they are not yet regarded as central or cornerstone notions. Recently the interest in comparing membrane systems and other models for concurrency has grown. In this paper we propose a translation of membrane system into zero safe nets and then we show how to associate an event automaton to the 1-unfolding of these nets. Thus we propose an event based view of computations of a membrane system

Dynamic Causality in Event Structures

Event Structures (ESs) address the representation of direct relationships between individual events, usually capturing the notions of causality and conflict. Up to now, such relationships have been static, i.e., they cannot change during a system run. Thus, the common ESs only model a static view on systems. We make causality dynamic by allowing causal dependencies between some events to be changed by occurrences of other events. We first model and study the case in which events may entail the removal of causal dependencies, then we consider the addition of causal dependencies, and finally we combine both approaches in the so-called Dynamic Causality ESs. For all three newly defined types of ESs, we study their expressive power in comparison to the well-known Prime ESs, Dual ESs, Extended Bundle ESs, and ESs for Resolvable Conflicts. Interestingly, Dynamic Causality ESs subsume Extended Bundle ESs and Dual ESs but are incomparable with ESs for Resolvable Conflicts

A Petri net view of covalent bonds

In nature and chemistry the interactions among elements often form bonds and among them covalent bonds are relevant, involving the sharing of electrons. Another relevant and compelling facet of calculi modelling covalent bonds is that certain steps in reactions are the result of concerting different activities, possibly reversing some of them. Starting from a calculus for covalent bonds, we investigate on how it can be done in a compositional fashion and how it can be encoded in suitable Petri nets. The outcome gives us a compositional covalent bond calculus and a truly distributed implementation. On these results it is possible to build a behavioural equivalence among terms.Fil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Mezzina, Claudio Antares. Università Degli Studi Di Urbino Carlo Bo; ItaliaFil: Pinna, G. Michele. Università degli Studi di Cagliari; Itali

Domain and Event Structure Semantics for Petri Nets with Read and Inhibitor Arcs

We propose a functorial concurrent semantics for Petri nets extended with read and inhibitor arcs, that we call inhibitor nets. Along the lines of the seminal work by Winskel on safe (ordinary) nets, the truly concurrent semantics is given at a categorical level via a chain of coreflections leading from the category SW-IN of semi-weighted inhibitor nets to the category Dom of finitary prime algebraic domains (equivalent to the category PES of prime event structures). As an intermediate semantic model, we introduce inhibitor event structures, an event-based model able to faithfully capture the dependencies among events which arise in the presence of read and inhibitor arcs. Inhibitor event structures generalise several event structure models in the literature, like prime, asymmetric and bundle event structures