Red-Green P Automata

In this short note we extend the notion of red-green Turing machines to speci c variants of P automata. Acceptance and recognizability of nite strings by red- green automata are de ned via in nite runs of the automaton on the input string and the way how to distinguish between red and green states

P and dP Automata: A Survey

This is a quick survey of basic notions and results related to P automata (P systems with symport/antiport rules working in the accepting mode), with some emphasis on the recently introduced dP automata (a distributed version of the standard P automata), ending with some open problems and research topics which we find of interest in this area.Junta de Andalucía P08 – TIC 0420

An infinite hierarchy of languages defined by dP systems

Here, we continue the study of the recently introduced dP automata. They are symport/antiport P systems consisting of a number of components, each one accepting a string, and working together in recognizing the concatenation of these separate strings; the overall string is distributed to the dP automaton components in a balanced way, i.e., in equal parts up to one symbol, like in the communication complexity area. The question whether or not the number of components induces an infinite hierarchy of the recognized languages was formulated as an open problem in the literature.Wesolve here affirmatively this question (by connecting P automata with right linear simple matrix grammars), then we also briefly discuss the relation between the balanced and the non-balanced way of splitting the input string among components; settling this latter problem remains as a research topic. Some other open problems are also formulated.Junta de Andalucía P08-TIC-0420

P automata revisited

We continue here the investigation of P automata, in their non-extended case, a class of devices which characterize non-universal family of languages. First, a recent conjecture is confirmed: any recursively enumerable language is obtained from a language recognized by a P automaton, to which an initial (arbitrarily large) string is added. Then, we discuss possibilities of extending P automata, following suggestions from string finite automata. For instance, automata with a memory (corresponding to push-down automata) are considered and their power is briefly investigated, as well as some closure properties of the family of languages recognized by P automata. In the context, a brief survey of results about P and dP automata (a distributed version of P automata) is provided, and several further research topics are formulated.Junta de Andalucía P08-TIC-0420

How to Go Beyond Turing with P Automata: Time Travels, Regular Observer !-Languages, and Partial Adult Halting

In this paper we investigate several variants of P automata having in nite runs on nite inputs. By imposing speci c conditions on the in nite evolution of the systems, it is easy to nd ways for going beyond Turing if we are watching the behavior of the systems on in nite runs. As speci c variants we introduce a new halting variant for P automata which we call partial adult halting with the meaning that a speci c prede ned part of the P automaton does not change any more from some moment on during the in nite run. In a more general way, we can assign !-languages as observer languages to the in nite runs of a P automaton. Speci c variants of regular !-languages then, for example, characterize the red-green P automata

Tissue-like P Systems with Channel-States

We consider tissue-like P systems with states associated with the links (we call them synapses) between cells, controlling the passage of objects across the links. We investigate the computing power of such devices for the case of using - in a sequential manner - antiport rules of small weights. Sys- tems with two cells are proven to be universal when having arbitrarily many states and minimal antiport rules, or two states, and antiport rules of weight two. Also the systems with arbitrarily many cells, three states, and minimal antiport rules are universal. In contrast, the systems with one cell and any number of states and rules of any weight only compute Parikh sets of ma- trix languages (generated by matrix grammars without appearance checking); characterizations of Parikh images of matrix languages are obtained for such one-cell systems with antiport rules of a reduced weight. A series of open problems are also formulated

Kernel P Systems Modelling, Testing and Veri cation

A kernel P system (kP system, for short) integrates in a coherent and elegant manner many of the P system features most successfully used for modelling various applications and, consequently, it provides a framework for analyzing these models. In this paper, we illustrate the modeling capabilities of kernel P systems by showing how other classes of P systems can be represented with this formalism and providing a number of kP system models for sorting algorithms. Furthermore, the problem of testing systems modelled as kP systems is also discussed and a test generation method based on automata is proposed. We also demonstrate how formal veri cation can be used to validate that the given models work as desired

Membrane computing: traces, neural inspired models, controls

Membrane Computing:Traces, Neural Inspired Models, ControlsAutor: Armand-Mihai IonescuDirectores: Dr. Victor Mitrana (URV)Dr. Takashi Yokomori (Universidad Waseda, Japón)Resumen Castellano:El presente trabajo está dedicado a una área muy activa del cálculo natural (que intenta descubrir la odalidad en la cual la naturaleza calcula, especialmente al nivel biológico), es decir el cálculo con membranas, y más preciso, a los modelos de membranas inspirados de la funcionalidad biológica de la neurona.La disertación contribuye al área de cálculo con membranas en tres direcciones principales. Primero, introducimos una nueva manera de definir el resultado de una computación siguiendo los rastros de un objeto especificado dentro de una estructura celular o de una estructura neuronal. A continuación, nos acercamos al ámbito de la biología del cerebro, con el objetivo de obtener varias maneras de controlar la computación por medio de procesos que inhiben/de-inhiben. Tercero, introducimos e investigamos en detallo - aunque en una fase preliminar porque muchos aspectos tienen que ser clarificados - una clase de sistemas inspirados de la manera en la cual las neuronas cooperan por medio de spikes, pulsos eléctricos de formas idénticas.English summary:The present work is dedicated to a very active branch of natural computing (which tries to discover the way nature computes, especially at a biological level), namely membrane computing, more precisely, to those models of membrane systems mainly inspired from the functioning of the neural cell.The present dissertation contributes to membrane computing in three main directions. First, we introduce a new way of defining the result of a computation by means of following the traces of a specified object within a cell structure or a neural structure. Then, we get closer to the biology of the brain, considering various ways to control the computation by means of inhibiting/de-inhibiting processes. Third, we introduce and investigate in a great - though preliminary, as many issues remain to be clarified - detail a class of P systems inspired from the way neurons cooperate by means of spikes, electrical pulses of identical shapes

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

Kernel P systems: from modelling to verification and testing

YesA kernel P system integrates in a coherent and elegant manner some of the most successfully used features of the P systems employed in modelling various applications. It also provides a theoretical framework for analysing these applications and a software environment for simulating and verifying them. In this paper, we illustrate the modelling capabilities of kernel P systems by showing how other classes of P systems can be represented with this formalism and providing a number of kernel P system models for a sorting algorithm and a broadcasting problem. We also show how formal verification can be used to validate that the given models work as desired. Finally, a test generation method based on automata is extended to non-deterministic kernel P systems.The work of MG, FI and RL were supported by a grant of the Romanian National Author- ity for Scientific Research, CNCS-UEFISCDI (project number: PN-II-ID-PCE-2011-3-0688); RCU