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

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

Event Structures with Disabling/Enabling relation and Event Automata

In recent years the consideration that events in evolutions of concurrent systems can happen with different histories has received ground. In particular the possibility that part of the history can be abstracted away or identified, like in the collective tokens philosophy for Petri Nets, has gained the stage. The various brands of event structures considered in literature are tailored to a fixed interpretation with respect to the history of an event. We investigate the adequateness of event structures with a disabling/enabling relation, to settle a common ground for the history dependent and history independent interpretations, and we establish a relationship between event automata and these notions of event structures