Computational Completeness of P Systems Using Maximal Variants of the Set Derivation Mode

We consider P systems only allowing rules to be used in at most one copy in each derivation step, especially the variant of the maximally parallel derivation mode where each rule may only be used at most once. Moreover, we also consider the derivation mode where from those sets of rules only those are taken which have the maximal number of rules. We check the computational completeness proofs of several variants of P systems and show that some of them even literally still hold true for the for these two new set derivation modes. Moreover, we establish two new results for P systems using target selection for the rules to be chosen together with these two new set derivation modes

Proceedings of the Workshop on Membrane Computing, WMC 2016.

yesThis Workshop on Membrane Computing, at the Conference of Unconventional Computation and Natural Computation (UCNC), 12th July 2016, Manchester, UK, is the second event of this type after the Workshop at UCNC 2015 in Auckland, New Zealand*. Following the tradition of the 2015 Workshop the Proceedings are published as technical report. The Workshop consisted of one invited talk and six contributed presentations (three full papers and three extended abstracts) covering a broad spectrum of topics in Membrane Computing, from computational and complexity theory to formal verification, simulation and applications in robotics. All these papers – see below, but the last extended abstract, are included in this volume. The invited talk given by Rudolf Freund, “P SystemsWorking in Set Modes”, presented a general overview on basic topics in the theory of Membrane Computing as well as new developments and future research directions in this area. Radu Nicolescu in “Distributed and Parallel Dynamic Programming Algorithms Modelled on cP Systems” presented an interesting dynamic programming algorithm in a distributed and parallel setting based on P systems enriched with adequate data structure and programming concepts representation. Omar Belingheri, Antonio E. Porreca and Claudio Zandron showed in “P Systems with Hybrid Sets” that P systems with negative multiplicities of objects are less powerful than Turing machines. Artiom Alhazov, Rudolf Freund and Sergiu Ivanov presented in “Extended Spiking Neural P Systems with States” new results regading the newly introduced topic of spiking neural P systems where states are considered. “Selection Criteria for Statistical Model Checker”, by Mehmet E. Bakir and Mike Stannett, presented some early experiments in selecting adequate statistical model checkers for biological systems modelled with P systems. In “Towards Agent-Based Simulation of Kernel P Systems using FLAME and FLAME GPU”, Raluca Lefticaru, Luis F. Macías-Ramos, Ionuţ M. Niculescu, Laurenţiu Mierlă presented some of the advatages of implementing kernel P systems simulations in FLAME. Andrei G. Florea and Cătălin Buiu, in “An Efficient Implementation and Integration of a P Colony Simulator for Swarm Robotics Applications" presented an interesting and efficient implementation based on P colonies for swarms of Kilobot robots. *http://ucnc15.wordpress.fos.auckland.ac.nz/workshop-on-membrane-computingwmc- at-the-conference-on-unconventional-computation-natural-computation

Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior

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

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

Towards Bridging Two Cell-Inspired Models: P Systems and R Systems

We examine, from the point of view of membrane computing, the two basic assumptions of reaction systems, the "threshold" and "no permanence" ones. In certain circumstances (e.g., defining the successful computations by local halting), the second assumption can be incorporated in a transition P system or in a symport/antiport P system without losing the universality. The case of the first postulate remains open: the reaction systems deal, deterministically, with finite sets of symbols, which is not of much interest for computing; three ways to introduce nondeterminism are suggested and left as research topics.Junta de Andalucía P08 – TIC 0420

Frontiers of Membrane Computing: Open Problems and Research Topics

This is a list of open problems and research topics collected after the Twelfth Conference on Membrane Computing, CMC 2012 (Fontainebleau, France (23 - 26 August 2011), meant initially to be a working material for Tenth Brainstorming Week on Membrane Computing, Sevilla, Spain (January 30 - February 3, 2012). The result was circulated in several versions before the brainstorming and then modified according to the discussions held in Sevilla and according to the progresses made during the meeting. In the present form, the list gives an image about key research directions currently active in membrane computing

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.Comment: 97 pages, 30 figure