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Computability
About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.
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01 Jan 2012
TL;DR: This book is very referred for you because it gives not only the experience but also lesson, it is about this book that will give wellness for all people from many societies.
Abstract: Where you can find the algorithmic randomness and complexity theory and applications of computability easily? Is it in the book store? On-line book store? are you sure? Keep in mind that you will find the book in this site. This book is very referred for you because it gives not only the experience but also lesson. The lessons are very valuable to serve for you, that's not about who are reading this algorithmic randomness and complexity theory and applications of computability book. It is about this book that will give wellness for all people from many societies.
221 citations
Book•
08 Sep 2008TL;DR: Many topics often absent from other textbooks, such as repetitions in words, state complexity, the interchange lemma, 2DPDAs, and the incompressibility method are covered here.
Abstract: Intended for graduate students and advanced undergraduates in computer science, A Second Course in Formal Languages and Automata Theory treats topics in the theory of computation not usually covered in a first course. After a review of basic concepts, the book covers combinatorics on words, regular languages, context-free languages, parsing and recognition, Turing machines, and other language classes. Many topics often absent from other textbooks, such as repetitions in words, state complexity, the interchange lemma, 2DPDAs, and the incompressibility method, are covered here. The author places particular emphasis on the resources needed to represent certain languages. The book also includes a diverse collection of more than 200 exercises, suggestions for term projects, and research problems that remain open.
218 citations
TL;DR: After a careful historical and conceptual analysis of computability and recursion, several recommendations are made about preserving the intensional differences between the concepts of “computability” and “recursion.”
Abstract: We consider the informal concept of “computability” or “effective calculability” and two of the formalisms commonly used to define it, “(Turing) computability” and “(general) recursiveness”. We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory, and its connection to other related areas. After a careful historical and conceptual analysis of computability and recursion we make several recommendations in section §7 about preserving the intensional differences between the concepts of “computability” and “recursion.” Specifically we recommend that: the term “recursive” should no longer carry the additional meaning of “computable” or “decidable;” functions defined using Turing machines, register machines, or their variants should be called “computable” rather than “recursive;” we should distinguish the intensional difference between Church's Thesis and Turing's Thesis, and use the latter particularly in dealing with mechanistic questions; the name of the subject should be “Computability Theory” or simply Computability rather than “Recursive Function Theory.”
218 citations