An infinite hierarchy induced by depth synchronization

AbstractDepth-synchronization measures the number of parallel derivation steps in a synchronized context-free (SCF) grammar. When not bounded by a constant the depth-synchronization measure of an SCF grammar is at least logarithmic and at most linear with respect to the word length. Languages with linear depth-synchronization measure and languages with a depth-synchronization measure in between logarithmic and linear are proven to exist. This gives rise to a strict infinite hierarchy within the family of SCF (and ET0L) languages

Decomposition and Descriptional Complexity of Shuffle on Words and Finite Languages

We investigate various questions related to the shuffle operation on words and finite languages. First we investigate a special variant of the shuffle decomposition problem for regular languages, namely, when the given regular language is the shuffle of finite languages. The shuffle decomposition into finite languages is, in general not unique. Thatis,therearelanguagesL^,L2,L3,L4withLiluL2= £3luT4but{L\,L2}^ {I/3, L4}. However, if all four languages are singletons (with at least two combined letters), it follows by a result of Berstel and Boasson [6], that the solution is unique; that is {L\,L2} = {L3,L4}. We extend this result to show that if L\ and L2 are arbitrary finite sets and Lz and Z-4 are singletons (with at least two letters in each), the solution is unique. This is as strong as it can be, since we provide examples showing that the solution can be non-unique already when (1) both L\ and L2 are singleton sets over different unary alphabets; or (2) L\ contains two words and L2 is singleton. We furthermore investigate the size of shuffle automata for words. It was shown by Campeanu, K. Salomaa and Yu in [11] that the minimal shuffle automaton of two regular languages requires 2mn states in the worst case (where the minimal automata of the two component languages had m and n states, respectively). It was also recently shown that there exist words u and v such that the minimal shuffle iii DFA for u and v requires an exponential number of states. We study the size of shuffle DFAs for restricted cases of words, namely when the words u and v are both periods of a common underlying word. We show that, when the underlying word obeys certain conditions, then the size of the minimal shuffle DFA for u and v is at most quadratic. Moreover we provide an efficient algorithm, which decides for a given DFA A and two words u and v, whether u lu u C L(A)

On the number of components in cooperating distributed grammar systems

AbstractIt is proved that the number of components in context-free cooperating distributed (CD) grammar systems can be reduced to 3 when they are working in the so-called sf-mode of derivation, which is the cooperation protocol which has been considered first for CD grammar systems. In this derivation mode, a component continues the derivation until and unless there is a nonterminal in the sentential form which cannot be rewritten according to that component. Moreover, it is shown that CD grammar systems in sf-mode with only one component can generate only the context-free languages but they can generate non-context-free languages if two components are used. The sf-mode of derivation is compared with other well-known cooperation protocols with respect to the hierarchies induced by the number of components

Finite Models of Splicing and Their Complexity

Durante las dos últimas décadas ha surgido una colaboración estrecha entre informáticos, bioquímicos y biólogos moleculares, que ha dado lugar a la investigación en un área conocida como la computación biomolecular. El trabajo en esta tesis pertenece a este área, y estudia un modelo de cómputo llamado sistema de empalme (splicing system). El empalme es el modelo formal del corte y de la recombinación de las moléculas de ADN bajo la influencia de las enzimas de la restricción.Esta tesis presenta el trabajo original en el campo de los sistemas de empalme, que, como ya indica el título, se puede dividir en dos partes. La primera parte introduce y estudia nuevos modelos finitos de empalme. La segunda investiga aspectos de complejidad (tanto computacional como descripcional) de los sistema de empalme. La principal contribución de la primera parte es que pone en duda la asunción general que una definición finita, más realista de sistemas de empalme es necesariamente débil desde un punto de vista computacional. Estudiamos varios modelos alternativos y demostramos que en muchos casos tienen más poder computacional. La segunda parte de la tesis explora otro territorio. El modelo de empalme se ha estudiado mucho respecto a su poder computacional, pero las consideraciones de complejidad no se han tratado apenas. Introducimos una noción de la complejidad temporal y espacial para los sistemas de empalme. Estas definiciones son utilizadas para definir y para caracterizar las clases de complejidad para los sistemas de empalme. Entre otros resultados, presentamos unas caracterizaciones exactas de las clases de empalme en términos de clases de máquina de Turing conocidas. Después, usando una nueva variante de sistemas de empalme, que acepta lenguajes en lugar de generarlos, demostramos que los sistemas de empalme se pueden usar para resolver problemas. Por último, definimos medidas de complejidad descriptional para los sistemas de empalme. Demostramos que en este respecto los sistemas de empalme finitos tienen buenas propiedades comparadosOver the last two decades, a tight collaboration has emerged between computer scientists, biochemists and molecular biologists, which has spurred research into an area known as DNAComputing (also biomolecular computing). The work in this thesis belongs to this field, and studies a computational model called splicing system. Splicing is the formal model of the cutting and recombination of DNA molecules under the influence of restriction enzymes.This thesis presents original work in the field of splicing systems, which, as the title already indicates, can be roughly divided into two parts: 'Finite models of splicing' on the onehand and 'their complexity' on the other. The main contribution of the first part is that it challenges the general assumption that a finite, more realistic definition of splicing is necessarily weal from a computational point of view. We propose and study various alternative models and show that in most cases they have more computational power, often reaching computational completeness. The second part explores other territory. Splicing research has been mainly focused on computational power, but complexity considerations have hardly been addressed. Here we introduce notions of time and space complexity for splicing systems. These definitions are used to characterize splicing complexity classes in terms of well known Turing machine classes. Then, using a new accepting variant of splicing systems, we show that they can also be used as problem solvers. Finally, we study descriptional complexity. We define measures of descriptional complexity for splicing systems and show that for representing regular languages they have good properties with respect to finite automata, especially in the accepting variant

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