[PDF] A Structural Theory For Varieties Of Tree Languages eBook

Author : Saeed Salehi
Publisher : VDM Verlag Dr. Muller
Page : 35 pages
File Size : 27,65 MB
Release : 2010-02
Category :
ISBN : 3639230558

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Trees are among the most fundamental and ubiquitous structures in mathematics and computer science. The notion of "tree" appears in many seemingly different areas from graph theory to universal algebra to logic. Tree languages and automata on trees have been studied extensively since the 1960s from both a purely mathematical and application point of view. Though the theory of tree automata and tree languages may have come into existence by generalizing string automata and languages, but it could not have stayed alive for long as a mere generalization. Apart from its intrinsic interest, this theory has found several applications and offers new perspectives to various parts of mathematical linguistics. It has been applied to the study of databases and XML schema languages, and provides tools for syntactic pattern recognition. When trees are defined as terms, universal algebra becomes directly applicable to tree automata and tree languages and, on the other hand, the theory of tree automata and tree languages suggests new notions and problems to universal algebra. In this book, the theory has been studied from the algebraic viewpoint.

Author : Valery B. Kudryavtsev
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 33,37 MB
Release : 2006-01-18
Category : Mathematics
ISBN : 1402038178

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Semigroups, Automata, Universal Algebra, Varieties

Author : Zoltán Ésik
Publisher : Springer
Page : 448 pages
File Size : 31,28 MB
Release : 2003-08-03
Category : Mathematics
ISBN : 3540450076

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The refereed proceedings of the 7th International Conference on Developments in Language Theory, DLT 2003, held in Szeged, Hungary, in July 2003. The 27 revised full papers presented together with 7 invited papers were carefully reviewed and selected from 57 submissions. All current aspects in language theory are addressed, in particular grammars, acceptors, and transducers for strings, trees, graphs, arrays, etc; algebraic theories for automata and languages; combinatorial properties of words and languages; formal power series; decision problems; efficient algorithms for automata and languages; and relations to complexity theory and logic, picture description and analysis, DNA computing, quantum computing, cryptography, and concurrency.

Author : Bakhadyr Khoussainov
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 32,18 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461201713

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The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.

Author : Henning Fernau
Publisher : Springer Nature
Page : 514 pages
File Size : 23,76 MB
Release : 2024
Category : Computer science
ISBN : 3031521137

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This book constitutes the proceedings of the 49th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2024, held in Cochem, Germany, in February 2024. The 33 full papers presented in this book were carefully reviewed and selected from 81 submissions. The book also contains one invited talk in full paper length. They focus on original research and challenges in foundations of computer science including algorithms, AI-based methods, computational complexity, and formal models.

Author : Tom Collins
Publisher : Springer
Page : 398 pages
File Size : 15,66 MB
Release : 2015-06-15
Category : Computers
ISBN : 3319206036

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This book constitutes the thoroughly refereed proceedings of the 5th International Conference on Mathematics and Computation in Music, MCM 2015, held in London, UK, in June 2015. The 24 full papers and 14 short papers presented were carefully reviewed and selected from 64 submissions. The papers feature research that combines mathematics or computation with music theory, music analysis, composition, and performance. They are organized in topical sections on notation and representation, music generation, patterns, performance, similarity and contrast, post-tonal music analysis, geometric approaches, deep learning, and scales.

Author : Samuel M. Scheiner
Publisher : University of Chicago Press
Page : 455 pages
File Size : 48,22 MB
Release : 2020-01-07
Category : Science
ISBN : 022667116X

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Darwin’s nineteenth-century writings laid the foundations for modern studies of evolution, and theoretical developments in the mid-twentieth century fostered the Modern Synthesis. Since that time, a great deal of new biological knowledge has been generated, including details of the genetic code, lateral gene transfer, and developmental constraints. Our improved understanding of these and many other phenomena have been working their way into evolutionary theory, changing it and improving its correspondence with evolution in nature. And while the study of evolution is thriving both as a basic science to understand the world and in its applications in agriculture, medicine, and public health, the broad scope of evolution—operating across genes, whole organisms, clades, and ecosystems—presents a significant challenge for researchers seeking to integrate abundant new data and content into a general theory of evolution. This book gives us that framework and synthesis for the twenty-first century. The Theory of Evolution presents a series of chapters by experts seeking this integration by addressing the current state of affairs across numerous fields within evolutionary biology, ranging from biogeography to multilevel selection, speciation, and macroevolutionary theory. By presenting current syntheses of evolution’s theoretical foundations and their growth in light of new datasets and analyses, this collection will enhance future research and understanding.

Author : Thomas Schwentick
Publisher : Springer
Page : 429 pages
File Size : 32,11 MB
Release : 2006-12-08
Category : Computers
ISBN : 3540692703

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This book constitutes the refereed proceedings of the 11th International Conference on Database Theory, ICDT 2007, held in Spain in January 2007. The papers are organized in topical sections on information integration and peer to peer, axiomatizations for XML, expressive power of query languages, incompleteness, inconsistency, and uncertainty, XML schemas and typechecking, stream processing and sequential query processing, ranking, XML update and query, as well as query containment.

Author : Sean A. Fulop
Publisher : Trafford Publishing
Page : 244 pages
File Size : 39,66 MB
Release : 2004
Category : Language Arts & Disciplines
ISBN : 1412023815

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This book presents the author's research on automatic learning procedures for categorial grammars of natural languages. The research program spans a number of intertwined disciplines, including syntax, semantics, learnability theory, logic, and computer science. The theoretical framework employed is an extension of categorial grammar that has come to be called multimodal or type-logical grammar. The first part of the book presents an expository summary of how grammatical sentences of any language can be deduced with a specially designed logical calculus that treats syntactic categories as its formulae. Some such Universal Type Logic is posited to underlie the human language faculty, and all linguistic variation is captured by the different systems of semantic and syntactic categories which are assigned in the lexicons of different languages. The remainder of the book is devoted to the explicit formal development of computer algorithms which can learn the lexicons of type logical grammars from learning samples of annotated sentences. The annotations consist of semantic terms expressed in the lambda calculus, and may also include an unlabeled tree-structuring over the sentence. The major features of the research include the following: We show how the assumption of a universal linguistic component---the logic of language---is not incompatible with the conviction that every language needs a different system of syntactic and semantic categories for its proper description. The supposedly universal linguistic categories descending from antiquity (noun, verb, etc.) are summarily discarded. Languages are here modeled as consisting primarily of sentence trees labeled with semantic structures; a new mathematical class of such term-labeled tree languages is developed which cross-cuts the well-known Chomsky hierarchy and provides a formal restrictive condition on the nature of human languages. The human language acquisition mechanism is postulated to be biased, such that it assumes all input language samples are drawn from the above "syntactically homogeneous" class; in this way, the universal features of human languages arise not just from the innate logic of language, but also from the innate biases which govern language learning. This project represents the first complete explicit attempt to model the aquisition of human language since Steve Pinker's groundbreaking 1984 publication, "Language Learnability and Language Development."