Computing with Membranes
01 Aug 2000-Journal of Computer and System Sciences (Academic Press, Inc.)-Vol. 61, Iss: 1, pp 108-143
TL;DR: It is proved that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice.
About: This article is published in Journal of Computer and System Sciences.The article was published on 2000-08-01 and is currently open access. It has received 2327 citations till now. The article focuses on the topics: Recursively enumerable language & Membrane computing.
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TL;DR: In this article, the authors introduce a class of neural-like P systems which they call spiking neural P systems (in short, SN P systems), in which the result of a computation is the time between the moments when a specified neuron spikes.
Abstract: This paper proposes a way to incorporate the idea of spiking neurons into the area of membrane computing, and to this aim we introduce a class of neural-like P systems which we call spiking neural P systems (in short, SN P systems). In these devices, the time (when the neurons fire and/or spike) plays an essential role. For instance, the result of a computation is the time between the moments when a specified neuron spikes. Seen as number computing devices, SN P systems are shown to be computationally complete (both in the generating and accepting modes, in the latter case also when restricting to deterministic systems). If the number of spikes present in the system is bounded, then the power of SN P systems falls drastically, and we get a characterization of semilinear sets. A series of research topics and open problems are formulated.
589 citations
TL;DR: It is argued here that artificial chemistries are the right stuff for the study of prebiotic and biochemical evolution, and they provide a productive framework for questions regarding the origin and evolution of organizations in general.
Abstract: This article reviews the growing body of scientific work in artificial chemistry. First, common motivations and fundamental concepts are introduced. Second, current research activities are discusse...
418 citations
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TL;DR: A computing model called a tissue P system is proposed, which processes symbols in a multiset rewriting sense, in a net of cells, which can simulate a Turing machine even when using a small number of cells.
Abstract: Starting from the way the inter-cellular communication takes place by means of protein channels (and also from the standard knowledge about neuron functioning), we propose a computing model called a tissue P system, which processes symbols in a multiset rewriting sense, in a net of cells. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses (“excitations”) to the neighboring cells. Such cell nets are shown to be rather powerful: they can simulate a Turing machine even when using a small number of cells, each of them having a small number of states. Moreover, in the case when each cell works in the maximal manner and it can excite all the cells to which it can send impulses, then one can easily solve the Hamiltonian Path Problem in linear time. A new characterization of the Parikh images of ET0L languages is also obtained in this framework. Besides such basic results, the paper provides a series of suggestions for further research.
412 citations
TL;DR: This work deals with several aspects concerning the formal verification of SN P systems and the computing power of some variants, and proposes a methodology based on the information given by the transition diagram associated with an SN P system which establishes the soundness and completeness of the system with respect to the problem it tries to resolve.
Abstract: This work deals with several aspects concerning the formal verification of SN P systems and the computing power of some variants. A methodology based on the information given by the transition diagram associated with an SN P system is presented. The analysis of the diagram cycles codifies invariants formulae which enable us to establish the soundness and completeness of the system with respect to the problem it tries to resolve. We also study the universality of asynchronous and sequential SN P systems and the capability these models have to generate certain classes of languages. Further, by making a slight modification to the standard SN P systems, we introduce a new variant of SN P systems with a special I/O mode, called SN P modules, and study their computing power. It is demonstrated that, as string language acceptors and transducers, SN P modules can simulate several types of computing devices such as finite automata, a-finite transducers, and systolic trellis automata.
408 citations
Cites methods from "Computing with Membranes"
...Keywords Spiking neural P system Formal verification Universality Asynchronous Sequential Finite automaton Finite state transducer Systolic trellis automaton...
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TL;DR: The K definition of Challenge, a programming language that aims at challenging and exposing the limitations of the various existing semantic frameworks, is proposed and discussed.
383 citations
Cites background from "Computing with Membranes"
...For each approach we list its main characteristics, its limitations, and its relationship with K....
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...Although context-sensitive rewriting might seem to be easily implementable by rewriting, in fact one has to perform an amount of “parsing” work linear in the size of the program for each computational step, like in small-step SOS....
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References
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