Minimal Parallelism and Number of Membrane Polarizations

It is known that the satisfiability problem (SAT) can be efficiently solved by a uniform family of P systems with active membranes that have two polarizations working in a maximally parallel way. We study P systems with active membranes without non-elementary membrane division, working in minimally parallel way. The main question we address is what number of polarizations is sufficient for an efficient computation depending on the types of rules used.In particular, we show that it is enough to have four polarizations, sequential evolution rules changing polarizations, polarizationless non-elementary membrane division rules and polarizationless rules of sending an object out. The same problem is solved with the standard evolution rules, rules of sending an object out and polarizationless non-elementary membrane division rules, with six polarizations. It is an open question whether these numbers are optimal

A Framework for Complexity Classes in Membrane Computing

The purpose of the present work is to give a general idea about the existing results and open problems concerning the study of complexity classes within the membrane computing framework. To this aim, membrane systems (seen as computing devices) are briefly introduced, providing the basic definition and summarizing the key ideas, trying to cover the various approaches that are under investigation in this area – of course, special attention is paid to the study of complexity classes. The paper concludes with some final remarks that hint the reasons why this field (as well as other unconventional models of computation) is attracting the attention of a growing community.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC-58

Polarizationless P Systems with Active Membranes Working in the Minimally Parallel Mode

We investigate the computing power and the efficiency of P systems with active membranes without polarizations, working in the minimally parallel mode. We prove that such systems are computationally complete and able to solve NP-complete problems even when the rules are of a restricted form, e.g., for establishing computational completeness we only need rules handling single objects and no division of non-elementary membranes is usedMinisterio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC 58

From distribution to replication in cooperative systems with active membranes: A frontier of the efficiency

P systems with active membranes use evolution, communication, dissolution and division(or separation) rules. They do not use cooperation neither priorities, but they haveelectrical charges associated with membranes, which can be modified by rule applications.The inspiration comes from the behaviourof living cells, who “compute” with theirproteins in order to obtain energy, create components, send information to other cells,kill themselves (in a process called apoptosis), and so on. In these models, mitosisissimulated by divisionrules (for elementary and non-elementary membranes) and meiosis,that is, membrane fission inspiration, is captured in separationrules. The parent’s objectsare replicated into both child membranes when a division occurs, while in the caseof separation, objects are distributed (according to a prefixed partition). In both cases,active membranes have been proved to be too powerful for solving computationally hardproblems in an efficient way. Due to this, polarizationless P systems withactive membraneshave been widely studied from a complexity point of view. Evolution rules simulate the transformation of components in membranes, but it iswell known that in Biology elements interact with each other in order to obtain newcomponents. In this paper, (restricted) cooperation in object evolution rules is considered,and the efficiency of the corresponding models is studied

On a Paun’s Conjecture in Membrane Systems

We study a P˘aun’s conjecture concerning the unsolvability of NP–complete problems by polarizationless P systems with active membranes in the usual framework, without cooperation, without priorities, without changing labels, using evolution, communication, dissolution and division rules, and working in maximal parallel manner. We also analyse a version of this conjecture where we consider polarizationless P systems working in the minimally parallel manner.Ministerio de Educación y Ciencia TIN2006–13425Junta de Andalucía TIC–58

Complexity aspects of polarizationless membrane systems

We investigate polarizationless P systems with active membranes working in maximally parallel manner, which do not make use of evolution or communication rules, in order to find which features are sufficient to efficiently solve computationally hard problems. We show that such systems are able to solve the PSPACE-complete problem QUANTIFIED 3-SAT, provided that non-elementary membrane division is controlled by the presence of a (possibly non-elementary) membrane.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58

On the Computational Efficiency of Polarizationless Recognizer P Systems with Strong Division and Dissolution

Recognizer P systems with active membranes have proven to be very powerful computing devices, being able to solve NP-complete decision problems in a polynomial time. However such solutions usually exploit many powerful features, such as electrical charges (polarizations) associated to membranes, evolution rules, communication rules, and strong or weak forms of division rules. In this paper we contribute to the study of the computational power of polarizationless recognizer P systems with active membranes. Precisely, we show that such systems are able to solve in polynomial time the NP-complete decision problem 3-sat by using only dissolution rules and a form of strong division for non–elementary membranes, working in the maximal parallel way

Simulation of Computing P Systems: A GPU Design for the Factorization Problem

Ministerio de Economía, Industria y Competitividad TIN2017-89842-P (MABICAP)Ministerio de Economía y Competitividad TIN2015-71562-RED

Design of Specific P Systems Simulators on GPUs

In order to validate P system models and to assist on their formal verification, simulators are indispensable. Moreover, having effi-cient simulation tools is crucial, and for this purpose, parallel platforms should be employed. So far, several parallel simulators for P systems have been developed, specifically targeting GPUs (Graphics Processing Units). Although being a hot topic within Membrane Computing, map-ping P system parallelism on GPUs is still not a mature area. In the past, we have successfully accelerated the simulation of two specific fam-ilies of P systems solving SAT with GPUs, and learned in the process some semantics ingredients that fit well on these parallel devices. We are extending this exploration by designing an specific simulator of a P system model for the FACTORIZATION problem. In this paper, we analyse the two main approaches for simulators, and depict some design decisions required for this case study.Ministerio de Industria, Economía y Competitividad TIN2017-89842-

Computing with cells: membrane systems - some complexity issues.

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism