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P Systems with Rule Production and Removal

Pan Linqiang, Song Bosheng

Fundamenta Informaticae

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2020

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Vol. 171, nr 1-4

313--329

EN

P systems are a class of parallel computational models inspired by the structure and functioning of living cells, where all the evolution rules used in a system are initially set up and keep unchanged during a computation. In this work, inspired by the fact that chemical reactions in a cell can be affected by both the contents of the cell and the environmental conditions, we introduce a variant of P systems, called P systems with rule production and removal (abbreviated as RPR P systems), where rules in a system are dynamically changed during a computation, that is, at any computation step new rules can be produced and some existing rules can be removed. The computational power of RPR P systems and catalytic RPR P systems is investigated. Specifically, it is proved that catalytic RPR P systems with one catalyst and one membrane are Turing universal; for purely catalytic RPR P systems, one membrane and two catalysts are enough for reaching Turing universality. Moreover, a uniform solution to the SAT problem is provided by using RPR P systems with membrane division. It is known that standard catalytic P systems with one catalyst and one membrane are not Turing universal. These results imply that rule production and removal is a powerful feature for the computational power of P systems.

2

Cooperation in Transport of Chemical Substances : A Complexity Approach within Membrane Computing

Valencia-Cabrera L., Orellana-Martín D., Martínez-del-Amor M. A., Riscos-Núñez A., Pérez-Jiménez M. J.

Fundamenta Informaticae

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2017

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Vol. 154, nr 1/4

373--385

EN

Membrane computing is a computing paradigm providing a class of distributed parallel computing devices of a biochemical type whose process units represent biological membranes. In the cell-like basic model, a hierarchical membrane structure formally described by a rooted tree is considered. It is well known that families of such systems where the number of membranes can only decrease during a computation (for instance by dissolving membranes), can only solve in polynomial time problems in class P. P systems with active membranes is a variant where membranes play a central role in their dynamics. In the seminal version, membranes have an electrical polarization (positive, negative, or neutral) associated in any instant, and besides being dissolved, they can also replicate by using division rules. These systems are computationally universal, that is, equivalent in power to deterministic Turing machines, and computationally efficient, that is, able to solve computationally hard problems in polynomial time. If polarizations in membranes are removed and dissolution rules are forbidden, then only problems in class P can be solved in polynomial time by these systems (even in the case when division rules for non-elementary membranes are permitted). In that framework it has been shown that by considering minimal cooperation (left-hand side of such rules consists of at most two symbols) and minimal production (only one object is produced by the application of such rules) in object evolution rules, such systems provide efficient solutions to NP-complete problems. In this paper, minimal cooperation and minimal production in communication rules instead of object evolution rules is studied, and the computational efficiency of these systems is obtained in the case where division rules for non-elementary membranes are permitted.

3

Computational Efficiency of Minimal Cooperation and Distribution in Polarizationless P Systems with Active Membranes

Valencia-Cabrera L., Orellana-Martín D., Martínez-del-Amor M. A., Riscos-Núñez A., Pérez-Jiménez M. J.

Fundamenta Informaticae

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2017

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Vol. 153, nr 1/2

147--172

EN

Polarizationless P systems with active membranes are non-cooperative systems, that is, the left-hand side of their rules have a single object. Usually, these systems make use of division rules as a mechanism to produce an exponential workspace in linear time. Division rules are inspired by cell division, a process of nuclear division that occurs when a parent cell divides to produce two identical daughter cells. On the other hand, separation rules are inspired by the membrane fission process, a mechanism by which a biological membrane is split into two new ones in such a manner that the contents of the initial membrane is distributed between the new membranes. In this paper, separation rules are used instead of division rules. The computational efficiency of these models is studied and the role of the (minimal) cooperation in object evolution rules is explored from a computational complexity point of view.

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An Optimal Frontier of the Efficiency of Tissue P Systems with Cell Separation

Pérez-Jiménez M. J., Sosík P.

Fundamenta Informaticae

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2015

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Vol. 138, nr 1/2

45--60

EN

A membrane system (P system) is a distributed computingmodel inspired by information processes in living cells. P systems previously provided new characterizations of a variety of complexity classes and their borderlines. Specifically, in tissue-like membrane systems, cell separation rules have been considered joint with communication rules of the form symport/antiport. On the one hand, only tractable problems can be efficiently solved by using cell separation and communication rules with length at most 2. On the other hand, an efficient and uniform solution to the SAT problem by using cell separation and communication rules with length at most 8 has been recently given. In this paper we improve the previous result by showing that the SAT problem can be solved by a family of tissue P systems with cell separation in linear time, by using communication rules with length at most 3. Thus, in the framework of tissue P systems with cell separation, we provide an optimal tractability borderline: passing from length 2 to 3 amounts to passing from non–efficiency to efficiency, assuming that P 6= NP.

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Looking for Small Efficient P Systems

Pérez-Jiménez M.J., Rius-Font M., Riscos-Nunez A., Romero-Campero F. J.

Fundamenta Informaticae

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2011

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Vol. 110, nr 1-4

293-308

EN

In 1936 A. Turing showed the existence of a universal machine able to simulate any Turing machine given its description. In 1956, C. Shannon formulated for the first time the problem of finding the smallest possible universal Turing machine according to some critera to measure its size such as the number of states and symbols. Within the framework ofMembrane Computing different studies have addressed this problem: small universal symport/antiport P systems (by considering the number of membranes, the weight of the rules and the number of objects as a measure of the size of the system), small universal splicing P systems (by considering the number of rules as a measure of the size of the system), and small universal spiking neural P systems (by considering the number of neurons as a measure of the size of the system). In this paper the problem of determining the smallest possible efficient P system is explicitly formulated. Efficiency within the framework of Membrane Computing refers to the capability of solving computationally hard problems (i.e. problems such that classical electronic computer cannot solve instances of medium/large size in any reasonable amount of time) in polynomial time. A descriptive measure to define precisely the notion of small P system is presented in this paper.