Accepting grammars and systems

We investigate several kinds of regulated rewriting (programmed, matrix, with regular control, ordered, and variants thereof) and of parallel rewriting mechanisms (Lindenmayer systems, uniformly limited Lindenmayer systems, limited Lindenmayer systems and scattered context grammars) as accepting devices, in contrast with the usual generating mode. In some cases, accepting mode turns out to be just as powerful as generating mode, e.g. within the grammars of the Chomsky hierarchy, within random context, regular control, L systems, uniformly limited L systems, scattered context. Most of these equivalences can be proved using a metatheorem on so-called context condition grammars. In case of matrix grammars and programmed grammars without appearance checking, a straightforward construction leads to the desired equivalence result. Interestingly, accepting devices are (strictly) more powerful than their generating counterparts in case of ordered grammars, programmed and matrix grammars with appearance checking (even programmed grammarsm with unconditional transfer), and 1lET0L systems. More precisely, if we admit erasing productions, we arrive at new characterizations of the recursivley enumerable languages, and if we do not admit them, we get new characterizations of the context-sensitive languages. Moreover, we supplement the published literature showing: - The emptiness and membership problems are recursivley solvable for generating ordered grammars, even if we admit erasing productions. - Uniformly limited propagating systems can be simulated by programmed grammars without erasing and without appearance checking, hence the emptiness and membership problems are recursively solvable for such systems. - We briefly discuss the degree of nondeterminism and the degree of synchronization for devices with limited parallelism

Membership for limited ET0L languages is not decidable

In this paper, we show how to encode arbitrary enumerable set of numbers given by register machines within limited EPT0L systems and programmed grammars with unconditional transfer.This result has various consequences, e.g.the existence of nonrecursive sets generable by 1lET0L systems or by programmed grammars with unconditional transfer. Moreover, ordered grammars are strictly less powerful than 1lET0L systems

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

Descriptional complexity of CD grammar systems

In der klassischen Theorie der formalen Sprachen gehört die Beschreibung von Sprachen durch Grammatiken oder Automaten zu den wichtigen Themen. Im Gegensatz zu diesen Modellen, die aus einer einzelnen Komponente bestehen, beschäftigt sich die Informatik heute aber immer häufiger mit verteilten Systemen, deren Komponenten auf verschiedene Art und Weise zusammenarbeiten. Eine Möglichkeit, dieses Konzept auf die Theorie der formalen Sprachen zu übertragen, ist die Definition von Grammatiksystemen. Ein Grammatiksystem besteht aus mehreren Grammatiken, die nach bestimmten Regeln zusammenarbeiten. Hauptsächlich unterscheidet man dabei zwischen sequentieller und paralleler Kooperation. In dieser Arbeitwerden kontextfreie „cooperating distributed“ (CD) Grammatiksysteme, ein Modell mit sequentieller Kooperation, betrachtet. Zur Erzeugung eines Wortes arbeiten dabei mehrere kontextfreie Grammatiken, die Komponenten, an einer gemeinsamen Satzform. Zu jedem Zeitpunkt ist immer nur eine einzige Komponente aktiv. Der Schwerpunkt der Arbeit liegt auf der Beschreibungskomplexität von CD Grammatiksystemen. Dabei wird zuerst auf die verschiedenen Maße für die Größe oder statische Komplexität eines CD Grammatiksystems eingegangen. Ein wichtiges Ergebnis im ersten Teil der Arbeit ist, daß man für CD Grammatiksysteme und insbesondere hybride CD Grammatiksysteme, eine Verallgemeinerung von kontextfreien CD Grammatiksystemen, einige dieser Maße nach oben beschränken kann. Darunter fallen die Anzahl der Komponenten und die maximale Anzahl von Produktionen in einer Komponente. Hält man einen der beiden Parameter fest, so entsteht eine unendliche Hierarchie über dem anderen Parameter. Der zweite Teil der Arbeit konzentriert sich darauf, Ergebnisse für Größenmaße zu erzielen, die nicht nur einzelne Aspekte der Komplexität, sondern die gesamte Größe oder Länge eines CD Grammatiksystems darstellen. Dafür werden CD Grammatiksysteme geeignet eingeschränkt. Man erhält metalineare Systeme und Systeme von endlichem Index. Im Gegensatz zum unbeschränkten Modell kann hier die generative Mächtigkeit sehr genau charakterisiert werden und es können Hilfsmittel wie Pumpinglemmata gezeigt werden.Weitere Resultate sind eine unendliche Hierarchie über der Breite beziehungsweise dem Index solcher Grammatiksysteme. Das wesentliches Resultat im zweiten Teil dieser Arbeit besteht daraus, daß zwischen zwei Klassen von diesen eingeschränkten CD Grammatiksystemen, deren entsprechende Sprachklassen echt ineinander enthalten sind, nichtrekursive Tradeoffs existieren. Das heißt, daß sich der Größenzuwachs beim Wechsel von der stärkeren Klasse von CD Grammatiksystemen in die schwächere durch keine rekursive Funktion beschränken läßt.Grammar systems are models of distributed systems in terms of formal grammars. They consist of several components where each component is a grammar. Apart from a parallel model in which the components contribute to a derivation simultaneously, there are sequential models, namely the cooperating distributed (CD) grammar systems. At one point of time only one component contributes to the derivation and is called the active component. The derivation mode defines how long productions of a component can be used and when the next component becomes active. When investigating classes of grammars, not only the generative capacity but also the conciseness and the simplicity of the description of the generated language classes are of interest. In case we can describe a class of languages with two different types of language generating devices, the question arises, whether there are differences concerning the size of the description. First, we investigate descriptional complexity aspects of hybrid CD grammar systems. In contrast to the general CD grammar system the components of a hybrid CD grammar systeme each have a derivation mode of their own. For some hybrid CD grammar systems it is possible to find equivalent systems that consist of only five components. For these hybrid CD grammar systems we can also construct equivalent systems with at most six productions in a component. If one of the two parameters is fixed, the other one induces an infinite hierarchy of language classes. Metalinear CD grammar systems are context-free CD grammar systems where each component consists of metalinear productions. The maximal number of nonterminals in all starting productions is referred to as the width of a CD grammar system. We show that between the class of CD grammar systems of width m+1 and of width m there are savings concerning the size of the grammar system not bounded by any recursive function. This is called a non-recursive trade-off. Furthermore, it is proven that there are non-recursive trade-offs between the class of metalinear CD grammar systems of width m and the class of (2m-1)-linear context-free grammars. In addition, some decidability results are presented. When we restrict a context-free CD grammar system in such a way that for each word w in the generated language there has to be at least one derivation where only m or less nonterminals are present in each sentential form, we obtain the class of CD grammar systems of index m. It is proven that between the language class generated by CD grammar systems of index m+1 and of index m there are savings concerning the size of the description not bounded by any recursive function. Additionally, it is shown that there are non-recursive trade-offs between the class of languages generated by CD grammar systems of index m and metalinear CD grammar systems of width m

Grammars with Restricted Derivation Trees

V této disertační práci jsou studovány teoretické vlastnosti gramatik s omezenými derivačními stromy. Po uvedení současného stavu poznání v této oblasti je výzkum zaměřen na tři základní typy omezení derivačních stromů. Nejprve je představeno zcela nové téma, které je založeno na omezení řezů a je zkoumána vyjadřovací síla takto omezené gramatiky. Poté je zkoumáno několik nových vlastností omezení kladeného na cestu derivačních stromů. Zejména je studován vliv vymazávacích pravidel na vyjadřovací sílu gramatik s omezenou cestou a pro tyto gramatiky jsou zavedeny dvě normální formy. Následně je popsána nová souvislost mezi gramatikami s omezenou cestou a některými pseudouzly. Dále je prezentován protiargument k vyjadřovací síle tohoto modelu, která byla dosud považována za dobře známou vlastnost. Nakonec je zavedeno zobecnění modelu s omezenou cestou na ne jednu, ale několik cest. Tento model je následně studován zejména z hlediska vlastností vkládání, uzávěrových vlastností a vlastností syntaktické analýzy.This doctoral thesis studies theoretical properties of grammars with restricted derivation trees. After presenting the state of the art concerning this investigation area, the research is focused on the three main kinds of the restrictions placed upon the derivation trees. First, it introduces completely new investigation area represented by cut-based restriction and examines the generative power of the grammars restricted in this way. Second, it investigates several new properties of path-based restriction placed upon the derivation trees. Specifically, it studies the impact of erasing productions on the generative power of grammars with restricted path and introduces two corresponding normal forms. Then, it describes a new relation between grammars with restricted path and some pseudoknots. Next, it presents a counterargument to the generative power of grammars with controlled path that has been considered as well-known so far. Finally, it introduces a generalization of path-based restriction to not just one but several paths. The model generalized in this way is studied, namely its pumping, closure, and parsing properties.