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    Dependencies and Symultaneity in Membrane Sys- tems

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    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 simultaneousl

    Modeling dependencies and simultaneity in membrane system computations

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    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 in a membrane and at a certain stage of the computation, which were the rules that produced it and subsequently (in a later step), which was the rule that consumed it. By recording the rules that have contributed to produce an object we can keep track of its history. Recording more than one rule for each object could be used to consider as equivalent some of the past histories, from the point of view of future use of this object. The other main ingredient in membrane system computations, namely the simultaneity in the rule applications, is usually enforced at the level of observation. We propose a way to look at it in a structural way. This is achieved using zero-safe nets that allows to synchronize transitions, i.e., rule occurrences. Zero-safe nets can be unfolded into causal nets in a classical way, and this unfolding can be manipulated to obtain a merged net where some histories could be considered as equivalent. To these notions of unfoldings, suitable event structures can be associated. The capability of capturing simultaneity of zero-safe nets is then transferred to the level of event structures by adding a way to express which events occur simultaneously. (C) 2011 Elsevier B.V. All rights reserved

    An Event Based Semantics of P-Systems

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    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
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