Membrane computing and complexity theory: A characterization of PSPACE
01 Feb 2007-Journal of Computer and System Sciences (Academic Press, Inc.)-Vol. 73, Iss: 1, pp 137-152
TL;DR: It is shown that confluent P systems with active membranes solve in polynomial time exactly the class of problems PSPACE, suggesting that the class PSPACE provides a tight upper bound on the computational potential of biological information processing models.
About: This article is published in Journal of Computer and System Sciences.The article was published on 2007-02-01 and is currently open access. It has received 88 citations till now. The article focuses on the topics: PSPACE & Membrane computing.
Citations
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01 Jan 2004
TL;DR: In this article, the authors add to tissue P systems the basic feature of (cell-like) P systems with active membranes -the possibility to divide cells, and illustrate this possibility with SAT problem.
Abstract: In tissue P systems several cells (elementary membranes) communicate through symport/antiport rules, thus carrying out a computation. We add to such systems the basic feature of (cell–like) P systems with active membranes – the possibility to divide cells. As expected (as it is the case for P systems with active membranes), in this way we get the possibility to solve computationally hard problems in polynomial time; we illustrate this possibility with SAT problem.
103 citations
TL;DR: This work adds to tissue P systems the basic feature of (cell–like) P systems with active membranes – the possibility to divide cells, and gets the possibility of solving computationally hard problems in polynomial time.
Abstract: In tissue P systems several cells (elementary membranes) communicate through symport/antiport rules, thus carrying out a computation. We add to such systems the basic feature of (cell–like) P systems with active membranes – the possibility to divide cells. As expected (as it is the case for P systems with active membranes), in this way we get the possibility to solve computationally hard problems in polynomial time; we illustrate this possibility with SAT problem.
99 citations
TL;DR: It turns out that the computational power of some systems is lowered from P to NL when using AC0-semi-uniformity, so it is argued that this is a more reasonable uniformity notion for these systems as well as others.
Abstract: We apply techniques from complexity theory to a model of biological cellular membranes known as membrane systems or P-systems. Like Boolean circuits, membrane systems are defined as uniform families of computational devices. To date, polynomial time uniformity has been the accepted uniformity notion for membrane systems. Here, we introduce the idea of using AC 0-uniformity and investigate the computational power of membrane systems under these tighter conditions. It turns out that the computational power of some systems is lowered from P to NL when using AC 0-semi-uniformity, so we argue that this is a more reasonable uniformity notion for these systems as well as others. Interestingly, other P-semi-uniform systems that are known to be lower-bounded by P are shown to retain their P lower-bound under the new tighter semi-uniformity condition. Similarly, a number of membrane systems that are known to solve PSPACE-complete problems retain their computational power under tighter uniformity conditions.
62 citations
Cites background from "Membrane computing and complexity t..."
...Similarly, a number of membrane systems that are known to solve PSPACE-complete problems retain their computational power under tighter uniformity conditions....
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...P-uniform families of active membrane systems (without charges) using non-elementary division (rules of type (f)) are known to characterise PSPACE [1, 15]....
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...P-uniform families of active membrane systems (without charges) using non-elementary division (rules of type (f)) are known to characterise PSPACE (Alhazov and PérezJiménez 2007; Sosı́k and Rodrı́guez-Patón 2007)....
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...Thus L-uniform families of AM0 systems using strong non-elementary division can solve at most PSPACE-complete problems (note that L(PSPACE)....
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...Clearly, the PSPACE upper-bound (Sosı́k and Rodrı́guez-Patón 2007) is unaffected if we restrict to AC0-uniformity....
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TL;DR: An efficient solution to the SAT problem is provided by means of a family of recognizer cell-like P systems with evolutional symport/antiport rules and membrane creation which make use of communication rules involving a restricted number of objects.
Abstract: Cell-like P systems with symport/antiport rules are computing models inspired by the conservation law, in the sense that they compute by changing the places of objects with respect to the membranes, and not by changing the objects themselves. In this work, a variant of these kinds of membrane systems, called cell-like P systems with evolutional symport/antiport rules, where objects can evolve in the execution of such rules, is introduced. Besides, inspired by the autopoiesis process (ability of a system to maintain itself), membrane creation rules are considered as an efficient mechanism to provide an exponential workspace in terms of membranes. The presumed efficiency of these computing models (ability to solve computationally hard problems in polynomial time and uniform way) is explored. Specifically, an efficient solution to the SAT problem is provided by means of a family of recognizer cell-like P systems with evolutional symport/antiport rules and membrane creation which make use of communication rules involving a restricted number of objects.
50 citations
TL;DR: This paper discusses research frontiers of membrane computing by presenting current open problems and research topics, together with the relevant background and motivation.
Abstract: This paper discusses research frontiers of membrane computing by presenting current open problems and research topics, together with the relevant background and motivation.
47 citations
References
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Book•
19 Dec 1990
TL;DR: The Handbook of Theoretical Computer Science provides professionals and students with a comprehensive overview of the main results and developments in this rapidly evolving field.
Abstract: "Of all the books I have covered in the Forum to date, this set is the most unique and possibly the most useful to the SIGACT community, in support both of teaching and research.... The books can be used by anyone wanting simply to gain an understanding of one of these areas, or by someone desiring to be in research in a topic, or by instructors wishing to find timely information on a subject they are teaching outside their major areas of expertise." -- Rocky Ross, "SIGACT News" "This is a reference which has a place in every computer science library." -- Raymond Lauzzana, "Languages of Design" The Handbook of Theoretical Computer Science provides professionals and students with a comprehensive overview of the main results and developments in this rapidly evolving field. Volume A covers models of computation, complexity theory, data structures, and efficient computation in many recognized subdisciplines of theoretical computer science. Volume B takes up the theory of automata and rewriting systems, the foundations of modern programming languages, and logics for program specification and verification, and presents several studies on the theoretic modeling of advanced information processing. The two volumes contain thirty-seven chapters, with extensive chapter references and individual tables of contents for each chapter. There are 5,387 entry subject indexes that include notational symbols, and a list of contributors and affiliations in each volume.
3,089 citations
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.
2,327 citations
"Membrane computing and complexity t..." refers background in this paper
...Keywords: Biological computation; P system; PSPACE; Alternating Turing machine...
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Book•
01 Jan 2002
TL;DR: This chapter discusses Membrane Computing, What It Is and What It is Not, and attempts to get back to reality with open problems and Universality results.
Abstract: Preface.- 1. Introduction: Membrane Computing, What It Is and What It Is Not.- 2. Prerequisites.- 3. Membrane Systems with Symbol-Objects.- 4. Trading Evolution for Communication.- 5. Structuring Objects.- 6. Networks of Membranes.- 7. Trading Space for Time.- 8. Further Technical Results.- 9. (Attempts to Get) Back to Reality.- Open Problems.- Universality Results. Bibliography.- Index.
1,760 citations
"Membrane computing and complexity t..." refers background in this paper
...Keywords: Biological computation; P system; PSPACE; Alternating Turing machine...
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...Membrane systems, called also P systems, are bio-inspired computing models belonging to a broader family of socalled biological or natural computing....
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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
"Membrane computing and complexity t..." refers background in this paper
...On the other hand, we conjecture that this operation can be substituted by other means as complex membrane signals, tissue organization of membranes [9] etc....
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Journal Article•
TL;DR: It is proved that a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects, is not only computationally universal, but also able to solve NP complete problems in polynomial time.
Abstract: P systems are parallel Molecular Computing models based on processing multisets of objects in cell-like membrane structures. Various variants were already shown to be computationally universal, equal in power to Turing machines. In this paper one proposes a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects. Moreover, the membranes can multiply themselves by division. We prove that this variant is not only computationally universal, but also able to solve NP complete problems in polynomial (actually, linear) time. We exemplify this assertion with the well-known SAT problem.
366 citations
"Membrane computing and complexity t..." refers background in this paper
...Keywords: Biological computation; P system; PSPACE; Alternating Turing machine...
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...Membrane systems, called also P systems, are bio-inspired computing models belonging to a broader family of socalled biological or natural computing....
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...Altogether, these studies suggest that the class PSPACE provides the tight upper bound on the computational potential of natural computing machinery....
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