Solving SAT with Antimatter in Membrane Computing

The set of NP-complete problems is split into weakly and strongly NP- complete ones. The di erence consists in the in uence of the encoding scheme of the input. In the case of weakly NP-complete problems, the intractability depends on the encoding scheme, whereas in the case of strongly NP-complete problems the problem is intractable even if all data are encoded in a unary way. The reference for strongly NP-complete problems is the Satis ability Problem (the SAT problem). In this paper, we provide a uniform family of P systems with active membranes which solves SAT { without polarizations, without dissolution, with division for elementary membranes and with matter/antimatter annihilation. To the best of our knowledge, it is the rst solution to a strongly NP-complete problem in this P system model.Ministerio de Economía y Competitividad TIN2012-3743

Recognizer P Systems with Antimatter

In this paper, we consider recognizer P systems with antimatter and the in uence of the matter/antimatter annihilation rules having weak priority over all the other rules or not. We rst provide a uniform family of P systems with active membranes which solves the strongly NP-complete problem SAT, the Satis ability Problem, without polarizations and without dissolution, yet with division for elementary membranes and with matter/antimatter annihilation rules having weak priority over all the other rules. Then we show that without this weak priority of the matter/antimatter annihilation rules over all the other rules we only obtain the complexity class PMinisterio de Economía y Competitividad TIN2012-3743

Counting Membrane Systems

A decision problem is one that has a yes/no answer, while a counting problem asks how many possible solutions exist associated with each instance. Every decision problem X has associated a counting problem, denoted by #X, in a natural way by replacing the question “is there a solution?” with “how many solutions are there?”. Counting problems are very attractive from a computational complexity point of view: if X is an NP-complete problem then the counting version #X is NP-hard, but the counting version of some problems in class P can also be NP-hard. In this paper, a new class of membrane systems is presented in order to provide a natural framework to solve counting problems. The class is inspired by a special kind of non-deterministic Turing machines, called counting Turing machines, introduced by L. Valiant. A polynomial-time and uniform solution to the counting version of the SAT problem (a well-known #P-complete problem) is also provided, by using a family of counting polarizationless P systems with active membranes, without dissolution rules and division rules for non-elementary membranes but where only very restrictive cooperation (minimal cooperation and minimal production) in object evolution rules is allowed

A Computational Complexity Theory in Membrane Computing

In this paper, a computational complexity theory within the framework of Membrane Computing is introduced. Polynomial complexity classes associated with di erent models of cell-like and tissue-like membrane systems are de ned and the most relevant results obtained so far are presented. Many attractive characterizations of P 6= NP conjecture within the framework of a bio-inspired and non-conventional computing model are deduced.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía P08–TIC-0420

Uniform Solution to QSAT Using Polarizationless Active Membranes

It is known that the satisfiability problem (SAT) can be solved a semi- uniform family of deterministic polarizationless P systems with active membranes with non-elementary membrane division. We present a double improvement of this result by showing that the satisfiability of a quantified boolean formula (QSAT) can be solved by a uniform family of P systems of the same kind.Ministerio de Educación y Ciencia TIN2005-09345-C04-0

Simulating a Family of Tissue P Systems Solving SAT on the GPU

In order to provide e cient software tools to deal with large membrane systems, high-throughput simulators are required. Parallel computing platforms are good candidates, since they are capable of partially implementing the inherently parallel nature of the model. In this concern, today GPUs (Graphics Processing Unit) are considered as highly parallel processors, and they are being consolidated as accelerators for scienti c applications. In fact, previous attempts to design P systems simulators on GPUs have shown that a parallel architecture is better suited in performance than traditional single CPUs. In 2010, a GPU-based simulator was introduced for a family of P systems with active membranes solving SAT in linear time. This is the starting point of this paper, which presents a new GPU simulator for another polynomial-time solution to SAT by means of tissue P systems with cell division, trading space for time. The aim of this simulator is to further study which ingredients of di erent P systems models are well suited to be managed by the GPU.Junta de Andalucía P08-TIC04200Ministerio de Economía y Competitividad TIN2012-3743

On the efficiency of cell-like and tissue-like recognizing membrane systems

Cell-like recognizing membrane systems are computational devices in the framework of membrane computing inspired from the structure of living cells, where biological membranes are arranged hierarchically. In this paper tissue-like recognizing membrane systems are presented. The idea is to consider that membranes are placed in the nodes of a graph, mimicking the cell intercommunication in tissues. In this context, polynomial complexity classes associated with recognizing membrane systems can be defined. We recall the definition for cell-like systems, and we introduce the corresponding complexity classes for the tissue-like case. Moreover, in this paper two efficient solutions to the satisfiability problem are analyzed and compared from a complexity point of view.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC-58

Evaluating space measures in P systems

P systems with active membranes are a variant of P systems where membranes can be created by division of existing membranes, thus creating an exponential amount of resources in a polynomial number of steps. Time and space complexity classes for active membrane systems have been introduced, to characterize classes of problems that can be solved by different membrane systems making use of different resources. In particular, space complexity classes introduced initially considered a hypothetical real implementation by means of biochemical materials, assuming that every single object or membrane requires some constant physical space (corresponding to unary notation). A different approach considered implementation of P systems in silico, allowing to store the multiplicity of each object in each membrane using binary numbers. In both cases, the elements contributing to the definition of the space required by a system (namely, the total number of membranes, the total number of objects, the types of different membranes, and the types of different objects) was considered as a whole. In this paper, we consider a different definition for space complexity classes in the framework of P systems, where each of the previous elements is considered independently. We review the principal results related to the solution of different computationally hard problems presented in the literature, highlighting the requirement of every single resource in each solution. A discussion concerning possible alternative solutions requiring different resources is presented

Cell-like and Tissue-like Membrane Systems as Recognizer Devices

Most of the variants of membrane systems found in the literature are generally thought as generating devices. In this paper recognizer computational devices (cell–like and tissue–like) are presented in the framework of Membrane Computing, using the biological membranes arranged hierarchically, inspired from the structure of the cell, and using the biological membranes placed in the nodes of a graph, inspired from the cell inter–communication in tissues. In this context, polynomial complexity classes of recognizer membrane systems are introduced. The paper also addresses the P versus NP problem, and the (efficient) solvability of computationally hard problems, in the framework of these new complexity classes.Ministerio de Educación y Ciencia TIN2005-09345-C04-0

Simulating a P system based efficient solution to SAT by using GPUs

P systems are inherently parallel and non-deterministic theoretical computing devices defined inside the field of Membrane Computing. Many P system simulators have been presented in this area, but they are inefficient since they cannot handle the parallelism of these devices. Nowadays, we are witnessing the consolidation of the GPUs as a parallel framework to compute general purpose applications. In this paper, we analyse GPUs as an alternative parallel architecture to improve the performance in the simulation of P systems, and we illustrate it by using the case study of a family of P systems that provides an efficient and uniform solution to the SAT problem. Firstly, we develop a simulator that fully simulates the computation of the P system, demonstrating that GPUs are well suited to simulate them. Then, we adapt this simulator to the GPU architecture idiosyncrasies, improving the performance of the previous simulator.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08–TIC-0420