New Versions of Classical Automata and Grammars

Tato diplomová práce se zabývá zkoumáním nových verzí automatů a gramatik a je proto rozdělena do dvou částí. První část definuje a studuje čisté více zásobníkové automaty a navíc zavádí úplná uspořádání nad jejich zásobníky nebo zásobníkovými symboly. Práce dokazuje, že zavedená omezení snižují vyjadřovací sílu automatů. Ve druhé části práce jsou definovány a popsány nové derivační módy gramatik s rozptýleným kontextem, které zobecňují relaci přímé derivace. Je dokázáno, že jejich použití nesnižuje vyjadřovací sílu gramatik.This master's thesis investigates new versions of automata and grammars and is thus divided into two parts. First part defines and studies pure multi-pushdown automata and additionally introduces total orders above their pushdowns or pushdown symbols. Present work proves, defined restrictions decrease accepting power of these automata. In the second part, new modes of scattered context derivations are defined and described, which generalize the relation of direct derivation. It is proved, these modes do not decrease the generation power of scattered context grammars.

An infinite hierarchy of language families generated by scattered context grammars with n-limited derivations

AbstractThis paper introduces scattered context grammars without erasing productions, in which an application of a production always occurs within the first n nonterminals of the current sentential form. It demonstrates that this restriction gives rise to an infinite hierarchy of language families each of which is properly included in the family of context-sensitive languages. In addition, it proves analogous results for unordered scattered context grammars. Some consequences of these results are derived and open problems formulated

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

Petri net controlled grammars

Different types of regulated grammars have been introduced in order to supplement shortcomings of context-free grammars in applications preserving their elegant mathematical properties. However, the rapid developments in present day industry, biology, and other areas challenge to deal with various tasks which need suitable tools for their modelling and investigation. We propose Petri net controlled grammars as models for representing and analyzing of metabolic pathways in living cells where Petri nets are responsible for the structure and communication of the pathways, and grammars represent biochemical processes. On the other hand, the control by Petri nets has also theoretical interest: it extends possibilities to introduce and investigate concurrent control mechanisms in formal language theory. The thesis introduces various variants of Petri net controlled grammars using different types of Petri nets and investigates their mathematical properties such as computational power and closure properties.Los diferentes tipos de gramáticas con reescritura regulada han sido introducidas para complementar las deficiencias de las gramáticas libres del contexto en las aplicaciones, preservando sus propiedades matemáticas. Por otro lado, la rápida evolución la biología, y otras áreas actuales supone un reto para tratar de las tareas varias que necesitan las herramientas adecuadas para la elaboración de modelos e investigación. Proponemos gramáticas controladas por redes de Petri como modelos para representar y analizar los procesos bioquímicos en las células vivas donde redes de Petri son responsables de la estructura, y gramáticas representan los procesos generativos. Además, el control de redes de Petri también tiene interés teórico: amplía las posibilidades de investigar los mecanismos de control concurrente en la teoría de lenguajes formales. La tesis presenta distintas variantes de gramáticas controladas por redes de Petri e investiga sus propiedades matemáticas

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.

Inferring Different Types of Lindenmayer Systems Using Artificial Intelligence

Lindenmayer systems (L-systems) are a formal grammar system which consist of a set of rewriting rules. Each rewriting rule is comprised of a symbol to replace (predecessor), a replacement string (successor), and an optional condition that is necessary for replacement. Starting with an initial string, every symbol in the string is replaced in parallel in accordance with the conditions on the rewriting rules, to produce a new string. The replacement process iterates as needed to produce a sequence of strings. There are different types of L-systems, which allow for different types of conditions, and methods of selecting the rules to apply. Some symbols of the alphabet can be interpreted as instructions for simulation software towards process modelling, where each string describes another step of the simulated process. Typically, creating an L-system for a specific process is done by experts by making meticulous measurements and using a priori knowledge about the process. It would be desirable to have a method to automatically learn the L-systems (the simulation program) from data, such as from a temporal sequence of images. This thesis presents a suite of tools, collectively called the Plant Model Inference Tools or PMIT (despite the name, the tools are domain agnostic), for inferring different types of L-systems using only a sequence of strings describing the process over some initial time period. Variants of PMIT are created for deterministic context-free L-systems, stochastic L-systems, and parametric L-systems. They are each evaluated using existing known deterministic and parametric L-systems from the literature, and procedurally generated stochastic L-systems. Accuracy can be detected in various ways, such as checking whether the inferred L-system is equal to the original one. PMIT is able to correctly infer deterministic L-systems with up to 31 symbols in the alphabet compared to the previous state-of-the-art algorithm's limit of 2 symbols. Stochastic L-systems allow symbols in the alphabet to have multiple rewriting rules each with an associated probability of being selected. Evaluating stochastic L-system inference with 960 procedurally generated L-systems with multiple sequences of strings as input found the following: 1) when 3 input sequences are used, the inferred successors always matched the original successors for systems with up to 9 rewriting rules, 2) when 6 sequences of strings are used, the difference between the associated probabilities of the inferred and the original L-system is approximately 1%. Parametric L-systems allow symbols to have multiple rewriting rules with parameters that get passed during rewriting. Rule selection is based on an associated Boolean condition over the parameters that gets evaluated to choose the rule to be applied. Inference is done in two steps. In the first step, the successors are inferred, and in the second step, appropriate Boolean conditions are found. Parametric L-system inference was evaluated on 20 known parametric L-systems. For 18 of the 20 L-systems where all successors were non-empty, the successors were correctly identified, but the time taken was up to 26 days on a single core CPU for the largest L-system. The second step, inferring the Boolean conditions, was successful for all 20 systems in the test set. No previous algorithm from the literature had implemented stochastic or parametric L-system inference. Inferring L-systems of greater complexity algorithmically can save considerable time and effort versus constructing them manually; however, perhaps more importantly rather than relying on existing knowledge, inferring a simulation of a process from data can help reveal the underlying scientific principles of the process