P systems with minimal parallelism

A current research topic in membrane computing is to find more realistic P systems from a biological point of view, and one target in this respect is to relax the condition of using the rules in a maximally parallel way. We contribute in this paper to this issue by considering the minimal parallelism of using the rules: if at least a rule from a set of rules associated with a membrane or a region can be used, then at least one rule from that membrane or region must be used, without any other restriction (e.g., more rules can be used, but we do not care how many). Weak as it might look, this minimal parallelism still leads to universality. We first prove this for the case of symport/antiport rules. The result is obtained both for generating and accepting P systems, in the latter case also for systems working deterministically. Then, we consider P systems with active membranes, and again the usual results are obtained: universality and the possibility to solve NP-complete problems in polynomial time (by trading space for time)

Generalized Communicating P Systems Working in Fair Sequential Model

In this article we consider a new derivation mode for generalized communicating P systems (GCPS) corresponding to the functioning of population protocols (PP) and based on the sequential derivation mode and a fairness condition. We show that PP can be seen as a particular variant of GCPS. We also consider a particular stochastic evolution satisfying the fairness condition and obtain that it corresponds to the run of a Gillespie's SSA. This permits to further describe the dynamics of GCPS by a system of ODEs when the population size goes to the infinity.Comment: Presented at MeCBIC 201

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

Catalytic and communicating Petri nets are Turing complete

In most studies about the expressiveness of Petri nets, the focus has been put either on adding suitable arcs or on assuring that a complete snapshot of the system can be obtained. While the former still complies with the intuition on Petri nets, the second is somehow an orthogonal approach, as Petri nets are distributed in nature. Here, inspired by membrane computing, we study some classes of Petri nets where the distribution is partially kept and which are still Turing complete

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

Solving complex problems with a bioinspired model

Membrane systems are parallel and bioinspired systems which simulate membranes behavior when processing information. As a part of unconventional computing, P-systems are proven to be effective in solvingcomplexproblems. A software technique is presented here that obtain good results when dealing with such problems. The rules application phase is studied and updated accordingly to obtain the desired results. Certain rules are candidate to be eliminated which can make the model improving in terms of time

Membrane Computing as a Modeling Framework. Cellular Systems Case Studies

Membrane computing is a branch of natural computing aiming to abstract computing models from the structure and functioning of the living cell, and from the way cells cooperate in tissues, organs, or other populations of cells. This research area developed very fast, both at the theoretical level and in what concerns the applications. After a very short description of the domain, we mention here the main areas where membrane computing was used as a framework for devising models (biology and bio-medicine, linguistics, economics, computer science, etc.), then we discuss in a certain detail the possibility of using membrane computing as a high level computational modeling framework for addressing structural and dynamical aspects of cellular systems. We close with a comprehensive bibliography of membrane computing applications

Investigating dynamic causalities in reaction systems

Reaction systems are a qualitative formalism for modeling systems of biochemical reactions characterized by the non-permanency of the elements: molecules disappear if not produced by any enabled reaction. Moreover, reaction systems execute in an environment that provides new molecules at each step. Brijder, Ehrenfeucht and Rozenberg investigated dynamic causalities in reaction systems by introducing the idea of predictors. A predictor of a molecule s, for a given n, is the set of molecules to be observed in the environment in order to determine whether s is produced or not by the system at step n. In this paper, we continue the investigation on dynamic causalities by defining an abstract interpretation framework containing three different notions of predictor: Formula based predictors, that is a propositional logic formula that precisely characterizes environments that lead to the production of s after n steps; Multi-step based predictors, that consist of n sets of molecules to be observed in the environment, one for each step; and Set based predictors, that are those proposed by Brijder, Ehrenfeucht and Rozenberg, and consist of a unique set of molecules to be observed in all steps. For each kind of predictor we define an effective operator that allows predictors to be computed for any molecule s and number of steps n. The abstract interpretation framework allows us to compare the three notions of predictor in terms of precision, to relate the three defined operators and to compute minimal predictors. We also discuss a generalization of this approach that allows predictors to be defined independently of the value of n, and a tabling approach for the practical use of predictors on reaction systems models. As an application, we use predictors, generalization and tabling to give theoretical grounds to previously obtained results on a model of gene regulation

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

Formal Verification of P Systems

Membrane systems, also known as P systems, constitute an innovative computational paradigm inspired by the structure and dynamics of the living cell. A P system consists of a hierarchical arrangement of compartments and a finite set of multiset rewriting and communication rules, which operate in a maximally parallel manner. The organic vision of concurrent dynamics captured by membrane systems stands in antithesis with conventional formal modelling methods which focus on algebraic descriptions of distributed systems. As a consequence, verifying such models in a mathematically rigorous way is often elusive and indeed counter-intuitive when considering established approaches, which generally require sequential process representations or highly abstract theoretical frameworks. The prevalent investigations with this objective in the field of membrane computing are ambivalent and inconclusive in the wider application scope of P systems. In this thesis we directly address the formal verification of membrane systems by means of model checking. A fundamental distinction between the agnostic perspective on parallelism, advocated by process calculi, and P systems' emblematic maximally parallel execution strategy is identified. On this basis, we establish that an intuitional translation to traditional process models is inadequate for the purpose of formal verification, due to a state space growth disparity. The observation is essential for this research project: on one hand it implies the feasibility of model checking P systems, and on the other hand it underlines the suitability of this formal verification technique in the context of membrane computing. Model checking entails an exhaustive state space exploration and does not derive inferences based on the independent instructions comprising a state transition. In this respect, we define a new sequential modelling strategy which is optimal for membrane systems and targets the SPIN formal verification tool. We introduce elementary P systems, a distributed computational model which subsumes the feature diversity of the membrane computing paradigm and distils its functional vocabulary. A suite of supporting software tools which gravitate around this formalism has also been developed, comprising of 1. the eps modelling language for elementary P systems; 2. a parser for the eps specification; 3. a model simulator and 4. a translation tool which targets the Promela specification of the SPIN model checker. The formal verification approach proposed in this thesis is progressively demonstrated in four heterogeneous case studies, featuring 1. a parallel algorithm applicable to a structured model; 2. a linear time solution to an NP-complete problem; 3. an innovative implementation of the Dining Philosophers scenario (a synchronisation problem) using an elementary P system and 4. a quantitative analysis of a simple random process implemented without the support of a probabilistic model