Modern Language Models And Computation

This textbook gives a systematized and compact summary, providing the most essential types of modern models for languages and computation together with their properties and applications. Most of these models properly reflect and formalize current computational methods, based on parallelism, distribution and cooperation covered in this book. As a result, it allows the user to develop, study, and improve these methods very effectively. This textbook also represents the first systematic treatment of modern language models for computation. It covers all essential theoretical topics concerning them. From a practical viewpoint, it describes various concepts, methods, algorithms, techniques, and software units based upon these models. Based upon them, it describes several applications in biology, linguistics, and computer science. Advanced-level students studying computer science, mathematics, linguistics and biology will find this textbook a valuable resource. Theoreticians, practitioners and researchers working in today’s theory of computation and its applications will also find this book essential as a reference.

This unique compendium highlights the theory of computation, particularly logic and automata theory. Special emphasis is on computer science applications including loop invariants, program correctness, logic programming and algorithmic proof techniques.This innovative volume differs from standard textbooks, by building on concepts in a different order, using fewer theorems with simpler proofs. It has added many new examples, problems and answers. It can be used as an undergraduate text at most universities.

This text makes in-depth explorations of a broad range of theoretical topics in computer science. It plunges into the applications of the abstract concepts in order to confront and address the skepticism of readers, and instill in them an appreciation for the usefulness of theory. A two-part presentation integrates logic and formal language—both with applications. Chapter topics cover mathematical preliminaries, propositional logic, proving things: why and how, predicate logic, proving with predicates, program verification, logic programming, language models for computer science, language models, finite automata and their languages, regular expressions, Lex: a tool for building lexical scanners, context-free grammars, pushdown automata and parsing, and turing machines. For future computer scientists.

Jumping Computation: Updating Automata and Grammars for Discontinuous Information Processing is primarily a theoretically oriented treatment of jumping automata and grammars, covering all essential theoretical topics concerning them, including their power, properties, and transformations. From a practical viewpoint, it describes various concepts, methods, algorithms, techniques, case studies and applications based upon these automata and grammars. In today’s computerized world, the scientific development and study of computation, referred to as the theory of computation, plays a crucial role. One important branch, language theory, investigates how to define and study languages and their models, which formalize algorithms according to which their computation is executed. These language-defining models are classified into two basic categories: automata, which define languages by recognizing their words, and grammars, which generate them. Introduced many decades ago, these rules reflect classical sequential computation. However, today’s computational methods frequently process information in a fundamentally different way, frequently “jumping” over large portions of the information as a whole. This book adapts classical models to formalize and study this kind of computation properly. Simply put, during their language-defining process, these adapted versions, called jumping automata and grammars, jump across the words they work on. The book selects important models and summarizes key results about them in a compact and uniform way. It relates each model to a particular form of modern computation, such as sequential, semi-parallel and totally parallel computation, and explains how the model in question properly reflects and formalizes the corresponding form of computation, thus allowing us to obtain a systematized body of mathematically precise knowledge concerning the jumping computation. The book pays a special attention to power, closure properties, and transformations, and also describes many algorithms that modify jumping grammars and automata so they satisfy some prescribed properties without changing the defined language. The book will be of great interest to anyone researching the theory of computation across the fields of computer science, mathematics, engineering, logic and linguistics.

A Concise Introduction to Computation Models and Computability Theory provides an introduction to the essential concepts in computability, using several models of computation, from the standard Turing Machines and Recursive Functions, to the modern computation models inspired by quantum physics. An in-depth analysis of the basic concepts underlying each model of computation is provided. Divided into two parts, the first highlights the traditional computation models used in the first studies on computability: - Automata and Turing Machines; - Recursive functions and the Lambda-Calculus; - Logic-based computation models. and the second part covers object-oriented and interaction-based models. There is also a chapter on concurrency, and a final chapter on emergent computation models inspired by quantum mechanics. At the end of each chapter there is a discussion on the use of computation models in the design of programming languages.

This handbook introduces a variety of concepts in discrete mathematics and mathematical modeling for languages and computation. The authors pay special attention to the implementation of mathematical concepts to explain clearly how to encode them in computational practice. All computer programs are written in C#.

Formal Languages and Computation: Models and Their Applications gives a clear, comprehensive introduction to formal language theory and its applications in computer science. It covers all rudimental topics concerning formal languages and their models, especially grammars and automata, and sketches the basic ideas underlying the theory of computation, including computability, decidability, and computational complexity. Emphasizing the relationship between theory and application, the book describes many real-world applications, including computer science engineering techniques for language processing and their implementation. Covers the theory of formal languages and their models, including all essential concepts and properties Explains how language models underlie language processors Pays a special attention to programming language analyzers, such as scanners and parsers, based on four language models—regular expressions, finite automata, context-free grammars, and pushdown automata Discusses the mathematical notion of a Turing machine as a universally accepted formalization of the intuitive notion of a procedure Reviews the general theory of computation, particularly computability and decidability Considers problem-deciding algorithms in terms of their computational complexity measured according to time and space requirements Points out that some problems are decidable in principle, but they are, in fact, intractable problems for absurdly high computational requirements of the algorithms that decide them In short, this book represents a theoretically oriented treatment of formal languages and their models with a focus on their applications. It introduces all formalisms concerning them with enough rigors to make all results quite clear and valid. Every complicated mathematical passage is preceded by its intuitive explanation so that even the most complex parts of the book are easy to grasp. After studying this book, both student and professional should be able to understand the fundamental theory of formal languages and computation, write language processors, and confidently follow most advanced books on the subject.