Formal Number Theory And Computability
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Formal Number Theory And Computability
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Author : Alec Fisher
language : en
Publisher: Oxford University Press, USA
Release Date : 1982
Formal Number Theory And Computability written by Alec Fisher and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
An Introduction To Formal Languages And Machine Computation
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Author : Song Y Yan
language : en
Publisher: World Scientific
Release Date : 1998-06-06
An Introduction To Formal Languages And Machine Computation written by Song Y Yan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-06-06 with Mathematics categories.
This book provides a concise and modern introduction to Formal Languages and Machine Computation, a group of disparate topics in the theory of computation, which includes formal languages, automata theory, turing machines, computability, complexity, number-theoretic computation, public-key cryptography, and some new models of computation, such as quantum and biological computation. As the theory of computation is a subject based on mathematics, a thorough introduction to a number of relevant mathematical topics, including mathematical logic, set theory, graph theory, modern abstract algebra, and particularly number theory, is given in the first chapter of the book. The book can be used either as a textbook for an undergraduate course, for a first-year graduate course, or as a basic reference in the field. Contents:Computation-Related Mathematics:Logics and ProofsSets, Functions and GraphsDivisibility, Continued Fractions and CongruencesGroups, Rings and FieldsFormal Languages and Automata:Languages, Grammars and AutomataFinite Automata and Regular LanguagesPush-Down Automata and Context-Free LanguagesTuring Machines and Recursively Enumerable LanguagesTuring Computability and Complexity:Computability and NoncomputabilityDecidability and UndecidabilityComputational ComplexityDesign and Analysis of AlgorithmsNumber-Theoretic Computations and Applications:Primality TestingInteger FactorizationDiscrete LogarithmsCryptology and Systems SecurityHigh-Speed ComputationThree More Applications in ComputingNew Models of Computation:Quantum ComputationBiological ComputationComparison of Quantum and DNA Biological ModelsComparison of Connectionist and DNA Biological Models Readership: Students, teachers and researchers in computer science. keywords:Formal Languages;Automata;Computability;Complexity;Models of Computation
Computability
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Author : Richard L Epstein
language : en
Publisher: Advanced Reasoning Forum
Release Date : 2018-10-24
Computability written by Richard L Epstein and has been published by Advanced Reasoning Forum this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Mathematics categories.
Now in a new edition!--the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".
Number Theory And Mathematical Logic
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Author : Open University Course Team
language : en
Publisher:
Release Date : 2004-01
Number Theory And Mathematical Logic written by Open University Course Team and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01 with Logic, Symbolic and mathematical categories.
In this unit we look at some theorems of a small but deeply significant fragment of number theory, called Q. We introduce the notion of a function being representable in a formal system. We shall discover that, although Q is quite a weak theory, it is sufficiently powerful to allow all total recursive functions (as discussed in unit ML03) to be representable in Q. This unit concludes with a discussion of diagonalization and Gödel's Diagonal Lemma.
Number Theory And Mathematical Logic
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Author : Open University Course Team
language : en
Publisher:
Release Date : 2004-01
Number Theory And Mathematical Logic written by Open University Course Team and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01 with Logic, Symbolic and mathematical categories.
In this unit we complete the description of the formal system started in units ML04 and ML05, and use the system to produce more complex formal proofs. We then discuss how to use it as a framework for proving theorems of number theory.
Sequences Groups And Number Theory
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Author : Valérie Berthé
language : en
Publisher: Birkhäuser
Release Date : 2019-02-02
Sequences Groups And Number Theory written by Valérie Berthé and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-02 with Mathematics categories.
This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.
Computability And Logic
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Author : George S. Boolos
language : en
Publisher: Cambridge University Press
Release Date : 2002-03-04
Computability And Logic written by George S. Boolos and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-04 with Mathematics categories.
This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book has become a classic because of its accessibility to students without a mathematical background, and because it covers not simply the staple topics of an intermediate logic course such as Godel's Incompleteness Theorems, but also a large number of optional topics from Turing's theory of computability to Ramsey's theorem. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer.
Formal Languages Automata And Numeration Systems 2
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Author : Michel Rigo
language : en
Publisher: John Wiley & Sons
Release Date : 2014-09-10
Formal Languages Automata And Numeration Systems 2 written by Michel Rigo and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-10 with Technology & Engineering categories.
The interplay between words, computability, algebra and arithmetic has now proved its relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite automata (such as that initiated by J.R. Büchi) or between combinatorics on words and number theory has paved the way to recent dramatic developments, for example, the transcendence results for the real numbers having a "simple" binary expansion, by B. Adamczewski and Y. Bugeaud. This book is at the heart of this interplay through a unified exposition. Objects are considered with a perspective that comes both from theoretical computer science and mathematics. Theoretical computer science offers here topics such as decision problems and recognizability issues, whereas mathematics offers concepts such as discrete dynamical systems. The main goal is to give a quick access, for students and researchers in mathematics or computer science, to actual research topics at the intersection between automata and formal language theory, number theory and combinatorics on words. The second of two volumes on this subject, this book covers regular languages, numeration systems, formal methods applied to decidability issues about infinite words and sets of numbers.
Formal Number Theory 1
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Author : Open University Course Team
language : en
Publisher:
Release Date : 2009-05-16
Formal Number Theory 1 written by Open University Course Team and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-16 with Logic, Symbolic and mathematical categories.
In this unit we complete the description of the formal system started in units ML04 and ML05, and use the system to produce more complex formal proofs. We then discuss how to use it as a framework for proving theorems of number theory.To order all 8 units in the Mathematical Logic series please see product M381/PP01
Cantorian Set Theory And Limitation Of Size
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Author : Michael Hallett
language : en
Publisher: Oxford University Press
Release Date : 1986
Cantorian Set Theory And Limitation Of Size written by Michael Hallett and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.