Further Twenty Six Open Problems in Membrane Computing
01 Jan 2005-pp 249-262
TL;DR: These notes follow the tradition of [16] and [18] – also combining their titles – having as the simple aim to challenge the reader – if not to address these problems, at least to produce his/her own list of problems and circulate it.
Abstract: These notes follow the tradition of [16] and [18] – also combining their titles. . . – having as the simple aim to challenge the reader – if not to address these problems, at least to produce his/her own list of problems and circulate it. Being a (more or less) personal list, the statements are somewhat elliptical and the references pretty scarce – and, of course, the selection is subjective. For technical and/or bibliographical details, one may consult the monograph [17], the recent volume [6], and, especially, the web page from http://psystems.disco.unimib.it. A very useful idea is to contact the people who have already worked about/around the problems, in order to get recent information and, the ultimate aim of these notes, to start collaborating. The last warning: the ordering of the problems has no significance (the labelling is only used for an easy reference), while including a problem in the present list does not mean that it is more important/interesting/challenging than any problem not
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TL;DR: Experimental results show that this evolutionary algorithm performs better than quantum-inspired evolutionary algorithms, for certain arrangements of the compartments of the P system structure utilized.
Abstract: This paper introduces an evolutionary algorithm which uses the concepts and principles of the quantum-inspired evolutionary approach and the hierarchical arrangement of the compartments of a P system. The P system framework is also used to formally specify this evolutionary algorithm. Extensive experiments are conducted on a well-known combinatorial optimization problem, the knapsack problem, to test the effectiveness of the approach. These experimental results show that this evolutionary algorithm performs better than quantum-inspired evolutionary algorithms, for certain arrangements of the compartments of the P system structure utilized.
(This work is supported by the National Natural Science Foundation of China (60702026, 60572143).)
111 citations
Cites background from "Further Twenty Six Open Problems in..."
...Thus, the possible interaction between P syst em and EAs, also mentioned by the list of twenty-six open problems in membrane computing [18], repre sents a fertile research field....
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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
Journal Article•
TL;DR: In this article, the authors give a historical overview of the most important results in the area of P systems and tissue P systems with symport/antiport rules, especially with respect to the development of computational completeness results improving descriptional complexity parameters.
Abstract: We first give a historical overview of the most important results obtained in the area of P systems and tissue P systems with symport/antiport rules, especially with respect to the development of computational completeness results improving descriptional complexity parameters. We consider the number of membranes (cells in tissue P systems), the weight of the rules, and the number of objects. Then we establish our newest results: P systems with only one membrane, symport rules of weight three, and with only seven additional objects remaining in the skin membrane at the end of a halting computation are computationally complete; P systems with minimal cooperation, i.e., P systems with symport/antiport rules of size one and P systems with symport rules of weight two, are computationally complete with only two membranes with only three and six, respectively, superfluous objects remaining in the output membrane at the end of a halting computation.
48 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
01 Jan 2012
TL;DR: A list of open problems and research topics collected after the Twelfth Conference on Membrane Computing, CMC 2012 (Fontainebleau, France) was meant initially to be a working material for the Tenth Brainstorming Week on MEMBRANE Computing, Sevilla, Spain (January 30 February 3, 2012) as mentioned in this paper.
Abstract: This is a list of open problems and research topics collected after the Twelfth Conference on Membrane Computing, CMC 2012 (Fontainebleau, France (23 26 August 2011), meant initially to be a working material for Tenth Brainstorming Week on Membrane Computing, Sevilla, Spain (January 30 February 3, 2012). The result was circulated in several versions before the brainstorming and then modified according to the discussions held in Sevilla and according to the progresses made during the meeting. In the present form, the list gives an image about key research directions currently active in membrane computing.
45 citations
References
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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
Journal Article•
215 citations
"Further Twenty Six Open Problems in..." refers background in this paper
...For technical and/or bibliographical details, one may consult the monograph [17], the recent volume [6], and, especially, the web page from http://psystems.disco.unimib.it....
[...]
02 Feb 2005
TL;DR: The number of catalysts in the original model of P systems with symbol objects introduced by Paun was shown to be computationally universal, provided that catalysts and priorities of rules are used; by reduction via register machines Sosik and Freund proved that the priorities may be omitted from the model without loss of computational power.
Abstract: The original model of P systems with symbol objects introduced by Paun was shown to be computationally universal, provided that catalysts and priorities of rules are used. By reduction via register machines Sosik and Freund proved that the priorities may be omitted from the model without loss of computational power. Freund, Oswald, and Sosik considered several variants of P systems with catalysts (but without priorities) and investigated the number of catalysts needed for these specific variants to be computationally universal. It was shown that for the classic model of P systems with the minimal number of two membranes the number of catalysts can be reduced from six to five; using the idea of final states the number of catalysts could even be reduced to four. In this paper we are able to reduce the number of catalysts again: two catalysts are already sufficient. For extended P systems we even need only one membrane and two catalysts. For the (purely) catalytic systems considered by Ibarra only three catalysts are already enough.
141 citations
Journal Article•
TL;DR: This paper partially confirms the conjecture proving that dissolving rules are not necessary for non-elementary membrane division, and the construction of a semi-uniform family of P systems is confirmed.
Abstract: P systems are parallel molecular computing models based on processing multisets of objects in cell-like membrane structures. Recently, Petr Sosik has shown that a semi-uniform family of P systems with active membranes and 2-division is able to solve the PSPACE-complete problem QBF-SAT in linear time; he has also conjectured that the membrane dissolving rules of the (d) type may be omitted, but probably not the (f) type rules for non-elementary membrane division. In this paper, we partially confirm the conjecture proving that dissolving rules are not necessary. Moreover, the construction is now uniform. It still remains open whether or not non-elementary membrane division is needed.
109 citations
TL;DR: It is shown that a uniformfamily of P systems with active membranes and 2-division is able to solve the well-known PSPACE-complete problem QBF inlinear time, implying that such a family of P system modelling celldivision is at least as powerful as so-called Second Machine Class computers.
Abstract: We study the computational power of cell division operations in the formal framework of P systems, a mathematical model of cell-like membrane structure with regulated transport of objects (molecules) through membranes. We show that a uniform family of P systems with active membranes and 2-division is able to solve the well-known PSPACE-complete problem QBF in linear time. This result implies that such a family of P systems modelling cell division is at least as powerful as so-called Second Machine Class computers. The Second Machine Class, containing most of the fundamental parallel computer models such as parallel RAM machines of types SIMD and MIMD, vector machines and others, is characterized by using an exponential amount of resources (processing units) with respect to the computing time.
84 citations
"Further Twenty Six Open Problems in..." refers background in this paper
...It seems that PSPACE ⊆ PMCcre, [23], too....
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...Which is the relation of PSPACE with the other three classes?...
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...It is an intriguing question here whether also PSPACE ⊆ PMCdiv−e holds (the conjecture was formulated – P. Sosik, M.J. Pérez–Jiménez – that this is not true; if confirmed, this will be a very interesting result, indeed, showing the need for the division of non-elementary membranes in order to cover PSPACE)....
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...B All the previous classes include NP, while from [26] (see also [4]) we know that PSPACE ⊆ PMCdiv−ne....
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