Characterizing Formality

Complexity classes are defined by quantitative restrictions of resources available to a computational model, like for instance the Turing machine. Contrarily, there is no obvious commonality in the definition of families of formal languages - instead they are described by example. This thesis is about the characterization of what makes a set of languages a family of formal languages. Families of formal languages, like for example the regular, context-free languages and their sub-families exhibit properties that are contrasted by the ones of complexity classes. Two of the properties families of formal languages seem to have is closure of intersection with regular languages, another is the existence of pumping or iteration arguments which yield the decidability of the emptiness. Complexity classes do not generally have a decidable emptiness, which lead us to a first candidate for the notion of formality - the decidability of the emptiness of regular intersection (intreg). We refute the decidability of intreg as a criterion by hiding the difficulty of deciding the emptiness of regular intersection: We show that for every decidable language L there is a language L' of essentially the same complexity such that intreg(L') is decidable. This implies that every complexity class contains complete languages for which the emptiness of regular intersection is decidable. An intermediate result we show is that the set of true quantified Boolean formulae has a decidable emptiness of regular intersection. As the known families of formal languages are all contained in NP, this yields a language (probably) outside of NP for which intreg is decidable, which additionally is a natural language in contrast to the artificial ones obtained by the hiding process. We introduce the notion of protocol languages which capture in some sense the behavior of a data-structure underlying the model of a formal language. They are defined in a fragment of second order logic, where the second order variables are uniquely determined by each word in the language and each letter implies a determined sub-structure of a word. Viewing the letters of a word as vertices and the successor as edges between them, each word can be seen as a path. The binary second order variables can be viewed as additional edges between word positions. Therefore, each word in a protocol language defines some unique graph. These graphs can be recognized by covering them with a predefined set of tiles which are node and edge-labeld graphs. Additional numerical constraints on the amount of each tile-type yields shrinking-arguments for protocol languages. If a word w in a protocol language exceeds a certain length such that the numerical constraints are (over-)satisfied, one can constuctively generate a shorter word w' from w that is also contained in the protocol language. We define logical extensions of protocol languages by allowing the conjunction of additional first order or monadic second order definable formulae and analyze the extensions in regard to trio operations. Protocol languages for the regular, context-free and indexed languages are exhibited -- for the first two we give protocol languages which act as generators for the respective family of formal languages. Finally, we show that the emptiness of protocol languages is decidable

Workshop on Formal Languages, Automata and Petri Nets

This report contains abstracts of the lectures presented at the workshop 'Formal Languages, Automata and Petri-Nets' held at the University of Stuttgart on January 16-17, 1998. The workshop brought together partners of the German-Hungarian project No. 233.6, Forschungszentrum Karlsruhe, Germany, and No. D/102, TeT Foundation, Budapest, Hungary. It provided an opportunity to present work supported by this project as well as related topics

Contributions of formal language theory to the study of dialogues

For more than 30 years, the problem of providing a formal framework for modeling dialogues has been a topic of great interest for the scientific areas of Linguistics, Philosophy, Cognitive Science, Formal Languages, Software Engineering and Artificial Intelligence. In the beginning the goal was to develop a "conversational computer", an automated system that could engage in a conversation in the same way as humans do. After studies showed the difficulties of achieving this goal Formal Language Theory and Artificial Intelligence have contributed to Dialogue Theory with the study and simulation of machine to machine and human to machine dialogues inspired by Linguistic studies of human interactions. The aim of our thesis is to propose a formal approach for the study of dialogues. Our work is an interdisciplinary one that connects theories and results in Dialogue Theory mainly from Formal Language Theory, but also from another areas like Artificial Intelligence, Linguistics and Multiprogramming. We contribute to Dialogue Theory by introducing a hierarchy of formal frameworks for the definition of protocols for dialogue interaction. Each framework defines a transition system in which dialogue protocols might be uniformly expressed and compared. The frameworks we propose are based on finite state transition systems and Grammar systems from Formal Language Theory and a multi-agent language for the specification of dialogue protocols from Artificial Intelligence. Grammar System Theory is a subfield of Formal Language Theory that studies how several (a finite number) of language defining devices (language processors or grammars) jointly develop a common symbolic environment (a string or a finite set of strings) by the application of language operations (for instance rewriting rules). For the frameworks we propose we study some of their formal properties, we compare their expressiveness, we investigate their practical application in Dialogue Theory and we analyze their connection with theories of human-like conversation from Linguistics. In addition we contribute to Grammar System Theory by proposing a new approach for the verification and derivation of Grammar systems. We analyze possible advantages of interpreting grammars as multiprograms that are susceptible of verification and derivation using the Owicki-Gries logic, a Hoare-based logic from the Multiprogramming field

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

Solutions of twisted word equations, EDT0L languages, and context-free groups

© Volker Diekert and Murray Elder; 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, F.4.2 Grammars and Other Rewriting Systems, F.4.3 Formal Languages. We prove that the full solution set of a twisted word equation with regular constraints is an EDT0L language. It follows that the set of solutions to equations with rational constraints in a contextfree group (= finitely generated virtually free group) in reduced normal forms is EDT0L. We can also decide whether or not the solution set is finite, which was an open problem. Moreover, this can all be done in PSPACE. Our results generalize the work by Lohrey and Sénizergues (ICALP 2006) and Dahmani and Guirardel (J. of Topology 2010) with respect to complexity and with respect to expressive power. Both papers show that satisfiability is decidable, but neither gave any concrete complexity bound. Our results concern all solutions, and give, in some sense, the "optimal" formal language characterization