Martin Davis on Computability, Computational Logic, and Mathematical Foundations, Omodeo Eugenio G., Policriti Alberto

Автор: Pour-El
Название: Computability in Analysis and Physics
ISBN: 1107168449 ISBN-13(EAN): 9781107168442
Издательство: Cambridge Academ
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Цена: 121440.00 T
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Описание: This is the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The authors are concerned with the computability or noncomputability of standard processes in analysis and physics. The book is self-contained and serves well as an introduction to research in this area.

Автор: Eugenio G. Omodeo; Alberto Policriti
Название: Martin Davis on Computability, Computational Logic, and Mathematical Foundations
ISBN: 3319418416 ISBN-13(EAN): 9783319418414
Издательство: Springer
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Цена: 111790.00 T
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Описание: This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability.

Автор: Merlin Carl
Название: Ordinal Computability: An Introduction to Infinitary Machines
ISBN: 3110495627 ISBN-13(EAN): 9783110495621
Издательство: Walter de Gruyter
Цена: 123910.00 T
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Описание: Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.

Автор: Rebecca Weber
Название: Computability Theory
ISBN: 082187392X ISBN-13(EAN): 9780821873922
Издательство: Mare Nostrum (Eurospan)
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Цена: 36960.00 T
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Описание: What can we compute--even with unlimited resources? Is everything within reach? Or are computations necessarily drastically limited, not just in practice, but theoretically? These questions are at the heart of computability theory. The goal of this book is to give the reader a firm grounding in the fundamentals of computability theory and an overview of currently active areas of research, such as reverse mathematics and algorithmic randomness. Turing machines and partial recursive functions are explored in detail, and vital tools and concepts including coding, uniformity, and diagonalization are described explicitly. From there the material continues with universal machines, the halting problem, parametrization and the recursion theorem, and thence to computability for sets, enumerability, and Turing reduction and degrees. A few more advanced topics round out the book before the chapter on areas of research. The text is designed to be self-contained, with an entire chapter of preliminary material including relations, recursion, induction, and logical and set notation and operators. That background, along with ample explanation, examples, exercises, and suggestions for further reading, make this book ideal for independent study or courses with few prerequisites.

Автор: Robič Borut
Название: The Foundations of Computability Theory
ISBN: 3662624206 ISBN-13(EAN): 9783662624203
Издательство: Springer
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Цена: 60550.00 T
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Описание:

Part I, The Roots of Computability Theory.- Introduction.- The Foundational Crisis of Mathematics.- Formalism.- Hilbert's Attempt at Recovery.- Part II, Classicial Computability Theory.- The Quest for a Formalization.- The Turing Machine.- The First Basic Results.- Incomputable Problems.- Methods of Proving Incomputability.- Part III, Relative Computability.- Computation with External Help.- Degrees of Unsolvability.- The Turing Hierarchy of Unsolvability.- The Class D of Degrees of Unsolvability.- C.E. Degrees and the Priority Method.- The Arithmetical Hierarchy.- Part IV, Back to the Roots.- Computability (Church-Turing) Thesis Revisited.- Further Reading.- App. A, Mathematical Background.- App. B, Notation Index.- Glossary.- References.- Index.

Автор: George S. Boolos
Название: Computability and logic
ISBN: 0521701465 ISBN-13(EAN): 9780521701464
Издательство: Cambridge Academ
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Цена: 33790.00 T
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Описание: Computability and Logic 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, but also a large number of optional topics, from Turing`s theory of computability to Ramsey`s theorem. This fifth edition was first published in 2007.

Автор: C.S. Calude; M.J. Dinneen; S. Sburlan
Название: Combinatorics, Computability and Logic
ISBN: 1852335262 ISBN-13(EAN): 9781852335267
Издательство: Springer
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Цена: 121110.00 T
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Описание: This volume contains the papers presented at the Third Combinatorics, Computability and Logic (DMTCS`01) conference, These papers cover topics such as abstract data types and specifications algorithms and data structures automata and formal languages computability among others.

Автор: Soare
Название: Turing Computability
ISBN: 3642319327 ISBN-13(EAN): 9783642319327
Издательство: Springer
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Цена: 69870.00 T
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Описание: Turing`s famous 1936 paper introduced a formal definition of a computing machine, a Turing machine. This book presents classical computability theory from Turing and Post to current results and methods, and their use in studying the information content of algebraic structures, models, and their relation to Peano arithmetic.

Автор: Sommaruga Giovanni, Strahm Thomas
Название: Turing`s Revolution: The Impact of His Ideas about Computability
ISBN: 3319793802 ISBN-13(EAN): 9783319793801
Издательство: Springer
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Цена: 111790.00 T
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Описание: This book provides an overview of the confluence of ideas in Turing`s era and work and examines the impact of his work on mathematical logic and theoretical computer science.

Автор: Centrone Stefania, Negri Sara, Sarikaya Deniz
Название: Mathesis Universalis, Computability and Proof
ISBN: 3030204499 ISBN-13(EAN): 9783030204495
Издательство: Springer
Цена: 111790.00 T
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Описание: 1. Introduction: Mathesis Universalis, Proof and ComputationStefania Centrone
2. Diplomacy of Trust in the European CrisisEnno Aufderheide
3. Mathesis Universalis and Homotopy Type TheorySteve Awodey
4. Note on the Benefit of Proof Representations by NameMatthias Baaz
5. Constructive Proofs of Negated StatementsJosef Berger and Gregor Svindland
6. Constructivism in Abstract MathematicsUlrich Berger
7. Addressing Circular Definitions via Systems of ProofsRiccardo Bruni
8. The Monotone Completeness Theorem in Constructive Reverse MathematicsHajime Ishihara and Takako Nemoto
9. From Mathesis Universalis to Fixed Points and Related Set-Theoretic ConceptsGerhard Jдger and Silvia Steila
10. Through an Inference Rule, DarklyRoman Kuznets
11. Objectivity and Truth in Mathematics: A Sober Non-Platonist PerspectiveGodehard Link
12. From Mathesis Universalis to Provability, Computability, and ConstructivityKlaus Mainzer
13. Analytic Equational Proof Systems for Combinatory Logic and λ-Calculus: a SurveyPierluigi Minari
14. Computational Interpretations of Classical Reasoning: From the Epsilon Calculus to Stateful ProgramsThomas Powell
15. The Concepts of Proof and GroundDag Prawitz
16. On Relating Theories: Proof-Theoretical ReductionMichael Rathjen and Michael Toppel
17. Program Extraction from Proofs: the Fan Theorem for Uniformly Coconvex BarsHelmut Schwichtenberg
18. Counting and Numbers, from Pure Mathesis to Base Conversion AlgorithmsJan von Plato
19. Point-Free Spectra of Linear SpreadsDaniel Wessel

Автор: Pippenger
Название: Theories of Computability
ISBN: 0521553806 ISBN-13(EAN): 9780521553803
Издательство: Cambridge Academ
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Цена: 98210.00 T
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Описание: This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only `the` theory of computability, but also a variety of other theories. Each topic is taken from the beginning and developed to a point at which the results can be appreciated.

Автор: Sernadas Amilcar, Sernadas Cristina, Rasga Joao
Название: A Mathematical Primer on Computability
ISBN: 1848902964 ISBN-13(EAN): 9781848902961
Издательство: Неизвестно
Цена: 26360.00 T
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Описание:

The book provides a self-contained introduction to computability theory for advanced undergraduate or early graduate students of mathematics and computer science. The technical material is illustrated with plenty of examples, problems with fully worked solutions as well as a range of proposed exercises.

Part I is centered around fundamental computability notions and results, starting with the pillar concepts of computational model (an abstract high-level programming language), computable function, decidable and listable set, proper universal function, decision problem and the reduction technique for transferring decidability and listability properties. The essential results namely Rice's Theorem, Rice-Shapiro's Theorem, Rice-Shapiro-McNaughton-Myhill's Theorem as well as Rogers' Theorem and the Recursion Theorem are presented and illustrated. Many-to-one reducibility and many-to-one degrees are investigated. A short introduction to computation with oracles is also included. Computable as well as non-computable operators are introduced as well as monotonic and finitary operators. The relationship between them is discussed, in particular via Myhill-Shepherdson's Theorem. Kleene's Least Fixed Point Theorem is also presented. Finally, Part I terminates with a briefi ng on the Turing computational model, Turing reducibility and Turing degrees.

Part II of the book concentrates on applications of computability in several areas namely in logic (undecidability of arithmetic, satisfiability in propositional logic, decidability in modal logic), Euclidean geometry, graphs and Kolmogorov complexity. Nevertheless no previous knowledge of these subjects is required. The essential details for understanding the applications are provided.