Trading Polarization for Bi-stable Catalysts in P Systems with Active Membranes

In the last time, several efforts have been made in order to remove polarizations of membranes from P systems with active membranes; the present paper is a contribution in this respect. In order to compensate the loss of power represented by avoiding polarizations, we use bi-stable catalysts. Polarizationless systems with active membranes which use bi-stable catalysts are proven to be computationally complete and able to solve efficiently NP-complete problems. In this paper we present a solution to SAT in linear time. In order to illustrate the presented solution, we also provide a simulation with CLIPS.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0

Reaching efficiency through collaboration in membrane systems: Dissolution, polarization and cooperation

From a computational complexity point of view, some syntactical ingredients play differentroles depending on the kind of combination considered. Inspired by the fact that the passing of a chemical substance through a biological membrane is often done by an interaction with the membrane itself, systems with active membranes were considered.Several combinations of different ingredients have been used in order to know which kindof problems could they solve efficientlyIn this paper, minimal cooperation with a minimal expression (the left-hand side of every object evolution rule has at most two objects and its right-hand side contains only one object) in object evolution rules is considered and a polynomial-time uniform solution to the SAT problem is presented. Consequently, a new way to tackle the P versus NP problem is provided.National Natural Science Foundation of China No 61472328National Natural Science Foundation of China No 6132010600

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

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

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

Computational Complexity Theory in Membrane Computing: Seventeen Years After

In this work we revisit the basic concepts, definitions of computational complexity theory in membrane computing. The paper also discusses a novel methodology to tackle the P versus NP problem in the context of the aforementioned theory. The methodology is illustrated with a collection of frontiers of tractability for several classes of P systems.Ministerio de Economía, Industria y Competitividad TIN2017-89842-

Communication in membrana Systems with symbol Objects.

Esta tesis está dedicada a los sistemas de membranas con objetos-símbolo como marco teórico de los sistemas paralelos y distribuidos de procesamiento de multiconjuntos.Una computación de parada puede aceptar, generar o procesar un número, un vector o una palabra; por tanto el sistema define globalmente (a través de los resultados de todas sus computaciones) un conjunto de números, de vectores, de palabras (es decir, un lenguaje), o bien una función. En esta tesis estudiamos la capacidad de estos sistemas para resolver problemas particulares, así como su potencia computacional. Por ejemplo, las familias de lenguajes definidas por diversas clases de estos sistemas se comparan con las familias clásicas, esto es, lenguajes regulares, independientes del contexto, generados por sistemas 0L tabulados extendidos, generados por gramáticas matriciales sin chequeo de apariciones, recursivamente enumerables, etc. Se prestará especial atención a la comunicación de objetos entre regiones y a las distintas formas de cooperación entre ellos.Se pretende (Sección 3.4) realizar una formalización los sistemas de membranas y construir una herramienta tipo software para la variante que usa cooperación no distribuida, el navegador de configuraciones, es decir, un simulador, en el cual el usuario selecciona la siguiente configuración entre todas las posibles, estando permitido volver hacia atrás. Se considerarán diversos modelos distribuidos. En el modelo de evolución y comunicación (Capítulo 4) separamos las reglas tipo-reescritura y las reglas de transporte (llamadas symport y antiport). Los sistemas de bombeo de protones (proton pumping, Secciones 4.8, 4.9) constituyen una variante de los sistemas de evolución y comunicación con un modo restrictivo de cooperación. Un modelo especial de computación con membranas es el modelo puramente comunicativo, en el cual los objetos traspasan juntos una membrana. Estudiamos la potencia computacional de las sistemas de membranas con symport/antiport de 2 o 3 objetos (Capítulo 5) y la potencia computacional de las sistemas de membranas con alfabeto limitado (Capítulo 6).El determinismo (Secciones 4.7, 5.5, etc.) es una característica especial (restrictiva) de los sistemas computacionales. Se pondrá especial énfasis en analizar si esta restricción reduce o no la potencia computacional de los mismos. Los resultados obtenidos para sistemas de bombeo del protones están transferidos (Sección 7.3) a sistemas con catalizadores bistabiles. Unos ejemplos de aplicación concreta de los sistemas de membranas (Secciones 7.1, 7.2) son la resolución de problemas NP-completos en tiempo polinomial y la resolución de problemas de ordenación.This thesis deals with membrane systems with symbol objects as a theoretical framework of distributed parallel multiset processing systems.A halting computation can accept, generate or process a number, a vector or a word, so the system globally defines (by the results of all its computations) a set of numbers or a set of vectors or a set of words, (i.e., a language), or a function. The ability of these systems to solve particular problems is investigated, as well as their computational power, e.g., the language families defined by different classes of these systems are compared to the classical ones, i.e., regular, context-free, languages generated by extended tabled 0L systems, languages generated by matrix grammars without appearance checking, recursively enumerable languages, etc. Special attention is paid to communication of objects between the regions and to the ways of cooperation between the objects.An attempt to formalize the membrane systems is made (Section 3.4), and a software tool is constructed for the non-distributed cooperative variant, the configuration browser, i.e., a simulator, where the user chooses the next configuration among the possible ones and can go back. Different distributed models are considered. In the evolution-communication model (Chapter 4) rewriting-like rules are separated from transport rules. Proton pumping systems (Sections 4.8, 4.9) are a variant of the evolution-communication systems with a restricted way of cooperation. A special membrane computing model is a purely communicative one: the objects are moved together through a membrane. We study the computational power of membrane systems with symport/antiport of 2 or 3 objects (Chapter 5) and the computational power of membrane systems with a limited alphabet (Chapter 6).Determinism (Sections 4.7, 5.5, etc.) is a special property of computational systems; the question of whether this restriction reduces the computational power is addressed. The results on proton pumping systems can be carried over (Section 7.3) to the systems with bi-stable catalysts. Some particular examples of membrane systems applications are solving NP-complete problems in polynomial time, and solving the sorting problem