Grammars with two-sided contexts

In a recent paper (M. Barash, A. Okhotin, "Defining contexts in context-free grammars", LATA 2012), the authors introduced an extension of the context-free grammars equipped with an operator for referring to the left context of the substring being defined. This paper proposes a more general model, in which context specifications may be two-sided, that is, both the left and the right contexts can be specified by the corresponding operators. The paper gives the definitions and establishes the basic theory of such grammars, leading to a normal form and a parsing algorithm working in time O(n^4), where n is the length of the input string.Comment: In Proceedings AFL 2014, arXiv:1405.527

Forgotten Islands of Regularity in Phonology

Open access publication of this volume supported by National Research, Development and Innovation Office grant NKFIH #120145 `Deep Learning of Morphological Structure'.Giving birth to Finite State Phonology is classically attributed to Johnson (1972), and Kaplan and Kay (1994). However, there is an ear- lier discovery that was very close to this achievement. In 1965, Hennie presented a very general sufficient condition for regularity of Turing machines. Although this discovery happened chronologically before Generative Phonology (Chomsky and Halle, 1968), it is a mystery why its relevance has not been realized until recently (Yli-Jyrä, 2017). The antique work of Hennie provides enough generality to advance even today’s frontier of finite-state phonology. First, it lets us construct a finite-state transducer from any grammar implemented by a tightly bounded one- tape Turing machine. If the machine runs in o(n log n), the construction is possible, and this case is reasonably decidable. Second, it can be used to model the regularity in context-sensitive derivations. For example, the suffixation in hunspell dictionaries (Németh et al., 2004) corresponds to time-bounded two-way computations performed by a Hennie machine. Thirdly, it challenges us to look for new forgotten islands of regularity where Hennie’s condition does not necessarily hold.Hennie presented a very general sufficient condition for regularity of Turing machines. This happened chronologically before Generative Phonology (Chomsky & Halle 1968) and the related finite-state research (Johnson 1972; Kaplan & Kay 1994). Hennie’s condition lets us (1) construct a finite-state transducer from any grammar implemented by a linear-time Turing machine, and (2) to model the regularity in context-sensitive derivations. For example, the suffixation in hunspell dictionaries (Németh et al. 2004) corresponds to time-bounded two way computations performed by a Hennie machine. Furthermore, it challenges us to look for new forgotten islands of regularity where Hennie’s condition does not necessarily hold.Peer reviewe

Clearing Restarting Automata

Restartovací automaty byly navrženy jako model pro redukční analýzu, která představuje lingvisticky motivovanou metodu pro kontrolu korektnosti věty. Cílem práce je studovat omezenější modely restartovacích automatů, které smí vymazat podřetězec nebo jej nahradit speciálním pomocným symbolem, jenom na základě omezeného lokálního kontextu tohoto podřetězce. Tyto restartovací automaty se nazývají clearing restarting automata. V práci jsou taktéž zkoumány uzávěrové vlastnosti těchto automatů, jejich vztah k Chomskeho hierarchii a možnosti učení těchto automatů na základě pozitivních a negativních příkladů.Restarting automata were introduced as a model for analysis by reduction which is a linguistically motivated method for checking correctness of a sentence. The goal of the thesis is to study more restricted models of restarting automata which based on a limited context can either delete a substring of the current content of its tape or replace a substring by a special symbol, which cannot be overwritten anymore, but it can be deleted later. Such restarting automata are called clearing restarting automata. The thesis investigates the properties of clearing restarting automata, their relation to Chomsky hierarchy and possibilities for machine learning of such automata from positive and negative samples.Department of Software and Computer Science EducationKatedra softwaru a výuky informatikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Complexity and modeling power of insertion-deletion systems

SISTEMAS DE INSERCIÓN Y BORRADO: COMPLEJIDAD Y CAPACIDAD DE MODELADO El objetivo central de la tesis es el estudio de los sistemas de inserción y borrado y su capacidad computacional. Más concretamente, estudiamos algunos modelos de generación de lenguaje que usan operaciones de reescritura de dos cadenas. También consideramos una variante distribuida de los sistemas de inserción y borrado en el sentido de que las reglas se separan entre un número finito de nodos de un grafo. Estos sistemas se denominan sistemas controlados mediante grafo, y aparecen en muchas áreas de la Informática, jugando un papel muy importante en los lenguajes formales, la lingüística y la bio-informática. Estudiamos la decidibilidad/ universalidad de nuestros modelos mediante la variación de los parámetros de tamaño del vector. Concretamente, damos respuesta a la cuestión más importante concerniente a la expresividad de la capacidad computacional: si nuestro modelo es equivalente a una máquina de Turing o no. Abordamos sistemáticamente las cuestiones sobre los tamaños mínimos de los sistemas con y sin control de grafo.COMPLEXITY AND MODELING POWER OF INSERTION-DELETION SYSTEMS The central object of the thesis are insertion-deletion systems and their computational power. More specifically, we study language generating models that use two string rewriting operations: contextual insertion and contextual deletion, and their extensions. We also consider a distributed variant of insertion-deletion systems in the sense that rules are separated among a finite number of nodes of a graph. Such systems are refereed as graph-controlled systems. These systems appear in many areas of Computer Science and they play an important role in formal languages, linguistics, and bio-informatics. We vary the parameters of the vector of size of insertion-deletion systems and we study decidability/universality of obtained models. More precisely, we answer the most important questions regarding the expressiveness of the computational model: whether our model is Turing equivalent or not. We systematically approach the questions about the minimal sizes of the insertiondeletion systems with and without the graph-control

Merkityn kaksoisnegaation sovellukset

Nested complementation plays an important role in expressing counter- i.e. star-free and first-order definable languages and their hierarchies. In addition, methods that compile phonological rules into finite-state networks use double-nested complementation or "double negation". This paper reviews how the double-nested complementation extends to a relatively new operation, generalized restriction (GR), coined by the author. ... The paper demonstrates that the GR operation has an interesting potential in expressing regular languages, various kinds of grammars, bimorphisms and relations. This motivates a further study of optimized implementation of the operation.Non peer reviewe