Streaming algorithms for language recognition problems

We study the complexity of the following problems in the streaming model. Membership testing for \DLIN We show that every language in \DLIN\ can be recognised by a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error, and by a deterministic p-pass $O(n/p)$ space algorithm. We show that these algorithms are optimal. Membership testing for \LL$(k)$ For languages generated by \LL$(k)$ grammars with a bound of $r$ on the number of nonterminals at any stage in the left-most derivation, we show that membership can be tested by a randomized one-pass $O(r\log n)$ space algorithm with inverse polynomial (in $n$) one-sided error. Membership testing for \DCFL We show that randomized algorithms as efficient as the ones described above for \DLIN\ and \LL(k) (which are subclasses of \DCFL) cannot exist for all of \DCFL: there is a language in \VPL\ (a subclass of \DCFL) for which any randomized p-pass algorithm with error bounded by $\epsilon < 1/2$ must use $\Omega(n/p)$ space. Degree sequence problem We study the problem of determining, given a sequence $d_1, d_2,..., d_n$ and a graph $G$, whether the degree sequence of $G$ is precisely $d_1, d_2,..., d_n$. We give a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error probability. We show that our algorithms are optimal. Our randomized algorithms are based on the recent work of Magniez et al. \cite{MMN09}; our lower bounds are obtained by considering related communication complexity problems

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

Regulated Formal Models and Their Reduction

Department of Theoretical Computer Science and Mathematical LogicKatedra teoretické informatiky a matematické logikyFaculty 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

生化学反応による計算能力の研究

早大学位記番号:新6514早稲田大

Syntax-based machine translation using dependency grammars and discriminative machine learning

Machine translation underwent huge improvements since the groundbreaking introduction of statistical methods in the early 2000s, going from very domain-specific systems that still performed relatively poorly despite the painstakingly crafting of thousands of ad-hoc rules, to general-purpose systems automatically trained on large collections of bilingual texts which manage to deliver understandable translations that convey the general meaning of the original input. These approaches however still perform quite below the level of human translators, typically failing to convey detailed meaning and register, and producing translations that, while readable, are often ungrammatical and unidiomatic. This quality gap, which is considerably large compared to most other natural language processing tasks, has been the focus of the research in recent years, with the development of increasingly sophisticated models that attempt to exploit the syntactical structure of human languages, leveraging the technology of statistical parsers, as well as advanced machine learning methods such as marging-based structured prediction algorithms and neural networks. The translation software itself became more complex in order to accommodate for the sophistication of these advanced models: the main translation engine (the decoder) is now often combined with a pre-processor which reorders the words of the source sentences to a target language word order, or with a post-processor that ranks and selects a translation according according to fine model from a list of candidate translations generated by a coarse model. In this thesis we investigate the statistical machine translation problem from various angles, focusing on translation from non-analytic languages whose syntax is best described by fluid non-projective dependency grammars rather than the relatively strict phrase-structure grammars or projectivedependency grammars which are most commonly used in the literature. We propose a framework for modeling word reordering phenomena between language pairs as transitions on non-projective source dependency parse graphs. We quantitatively characterize reordering phenomena for the German-to-English language pair as captured by this framework, specifically investigating the incidence and effects of the non-projectivity of source syntax and the non-locality of word movement w.r.t. the graph structure. We evaluated several variants of hand-coded pre-ordering rules in order to assess the impact of these phenomena on translation quality. We propose a class of dependency-based source pre-ordering approaches that reorder sentences based on a flexible models trained by SVMs and and several recurrent neural network architectures. We also propose a class of translation reranking models, both syntax-free and source dependency-based, which make use of a type of neural networks known as graph echo state networks which is highly flexible and requires extremely little training resources, overcoming one of the main limitations of neural network models for natural language processing tasks