Tissue P systems with cell division

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.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

Tissue P Systems with Cell Division

In tissue P systems several cells (elementary membranes) commu- nicate through symport/antiport rules, thus carrying out a computation. We add to such systems the basic feature of (cell) 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 computa- tionally hard problems in polynomial time; we illustrate this possibility with SAT problem.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

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

In the framework of tissue P systems with cell division, the length of communication rules provides a frontier for the tractability of decision problems. On the one hand, the limitation on the efficiency of tissue P systems with cell division and communication rules of length 1 has been established. On the other hand, polynomial time solutions to NP–complete problems by using families of tissue P systems with cell division and communication rules of length at most 3 has been provided. In this paper, we improve the previous result by showing that the HAM-CYCLE problem can be solved in polynomial time by a family of tissue P systems with cell division by using communication rules with length at most 2. Hence, a new tractability boundary is given: passing from 1 to 2 amounts to passing from non–efficiency to efficiency, assuming that P ̸= NP.Ministerio de Ciencia e Innovación TIN2009-13192Junta de Andalucía P08 – TIC 0420

Descriptional Complexity of Tissue-Like P Systems with Cell Division

In this paper we address the problem of describing the complexity of the evolution of a tissue-like P system with cell division. In the computations of such systems the number of (parallel) steps is not sufficient to evaluate the complexity. Following this consideration, Sevilla Carpets were introduced as a tool to describe the space-time complexity of P systems. Sevilla Carpets have already been used to compare two different solutions of the Subset Sum problem (both designed in the framework of P systems with active membranes) running on the same instance. In this paper we extend the comparison to the framework of tissue-like P systems with cell division.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420

Solving Common Algorithmic Problem by Recognizer Tissue P Systems

Common Algorithmic Problem is an optimization problem, which has the nice property that several other NP-complete problems can be reduced to it in linear time. In this work, we deal with its decision version in the framework of tissue P systems. A tissue P system with cell division is a computing model which has two types of rules: communication and division rules. The ability of cell division allows us to obtain an exponential amount of cells in linear time and to design cellular solutions to computationally hard problems in polynomial time. We here present an effective solution to Common Algorithmic Decision Problem by using a family of recognizer tissue P systems with cell division. Furthermore, a formal verification of this solution is given.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08-TIC-0420

Limits of the power of Tissue P systems with cell division

Tissue P systems generalize the membrane structure tree usual in original models of P systems to an arbitrary graph. Basic opera- tions in these systems are communication rules, enriched in some variants with cell division or cell separation. Several variants of tissue P systems were recently studied, together with the concept of uniform families of these systems. Their computational power was shown to range between P and NP ? co-NP , thus characterizing some interesting borderlines between tractability and intractability. In this paper we show that com- putational power of these uniform families in polynomial time is limited by the class PSPACE . This class characterizes the power of many clas- sical parallel computing model

(Tissue) P Systems with Anti-Membranes

The concept of a matter object being annihilated when meeting its corresponding anti-matter object is taken over for membranes as objects and anti-membranes as the corresponding annihilation counterpart in P systems. Natural numbers can be represented by the corresponding number of membranes with a speci c label. Computational completeness in this setting then can be obtained with using only elementary membrane division rules, without using objects. A similar result can be obtained for tissue P systems with cell division rules and cell / anti-cell annihilation rules. In both cases, as derivation modes we may take the standard maximally parallel derivation modes as well as any of the maximally parallel set derivation modes (non-extendable (multi)sets of rules, (multi)sets with maximal number of rules, (multi)sets of rules a ecting the maximal number of objects)

The Role of the Environment in Tissue P Systems with Cell Division

Classical tissue P systems with cell division have a special alphabet whose elements appear at the initial configuration of the system in an arbitrary large number of copies. These objects are shared in a distinguished place of the system, called the environment. Besides, the ability of these computing devices to have infinite copies of some objects has been widely exploited in the design of efficient solutions to computationally hard problems. This paper deals with computational aspects of tissue P systems with cell division where there is not an environment having the property mentioned above. Specifically, we establish the relationships between the polynomial complexity class associated with tissue P systems with cell division and with or without environment. As a consequence, we prove that it is not necessary to have infinite copies of some objects at the initial configuration in order to solve NP–complete problems in an efficient way.Ministerio de Ciencia e Innovación TIN2009-13192Junta de Andalucía P08 – TIC 0420

Solving Subset Sum in Linear Time by Using Tissue P Systems with Cell Division

Tissue P systems with cell division is a computing model in the framework of Membrane Computing based on intercellular communication and cooperation between neurons. The ability of cell division allows us to obtain an exponential amount of cells in linear time and to design cellular solutions to NP-complete problems in polynomial time. In this paper we present a solution to the Subset Sum problem via a family of such devices. This is the first solution to a numerical NP-complete problem by using tissue P systems with cell division.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58