Dependencies and Simultaneity in Membrane Systems

TL;DR

This paper introduces a novel approach using zero-safe nets and event structures to analyze and represent the simultaneity of rule applications in membrane system computations, enhancing the understanding of their concurrent behavior.

Contribution

It proposes a new method to model and analyze the simultaneity in membrane systems using zero-safe nets and event structures, extending beyond traditional dependency analysis.

Findings

Zero-safe nets effectively model synchronization of rule applications.

Event structures can express simultaneous events in membrane systems.

The approach provides a refined view of membrane system concurrency.

Abstract

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.