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.
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: Pour-El Название: Computability in Analysis and Physics ISBN: 1107168449 ISBN-13(EAN): 9781107168442 Издательство: Cambridge Academ Рейтинг: Цена: 18216.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Robič Borut Название: The Foundations of Computability Theory ISBN: 3662624206 ISBN-13(EAN): 9783662624203 Издательство: Springer Рейтинг: Цена: 9083.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
Название: Structure and randomness in computability and set theory ISBN: 9813228229 ISBN-13(EAN): 9789813228221 Издательство: World Scientific Publishing Рейтинг: Цена: 19008.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This volume presents some exciting new developments occurring on the interface between set theory and computability as well as their applications in algebra, analysis and topology. These include effective versions of Borel equivalence, Borel reducibility and Borel determinacy. It also covers algorithmic randomness and dimension, Ramsey sets and Ramsey spaces. Many of these topics are being discussed in the NSF-supported annual Southeastern Logic Symposium.
Contents: Limits of the Kucerea-Gacs Coding Method (George Barmpalias and Andrew Lewis-Pye); Infinitary partition properties of sums of selective ultrafilters (Andreas Blass); Semiselective Coideals and Ramsey Sets (Carlos DiPrisco and Leonardo Pacheco); Survey on Topological Ramsey Spaces Dense in Forcings (Natasha Dobrinen); Higher Computability in the Reverse Mathematics of Borel Determinacy (Sherwood Hachtman); Computability and Definability (Valentina Harizanov); A Ramsey Space of Infinite Polyhedra and the Random Polyhedron (Jose G Mijares Palacios and Gabriel Padilla); Computable Reducibility for Cantor Space (Russell G Miller); Information vs Dimension - An Algorithmic Perspective (Jan Reimann);
Readership: Graduate students and researchers interested in the interface between set theory and computability.
Автор: George S. Boolos Название: Computability and logic ISBN: 0521701465 ISBN-13(EAN): 9780521701464 Издательство: Cambridge Academ Рейтинг: Цена: 5069.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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 Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Sommaruga Giovanni, Strahm Thomas Название: Turing`s Revolution: The Impact of His Ideas about Computability ISBN: 3319793802 ISBN-13(EAN): 9783319793801 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Pippenger Название: Theories of Computability ISBN: 0521553806 ISBN-13(EAN): 9780521553803 Издательство: Cambridge Academ Рейтинг: Цена: 14731.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: 3954.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
Автор: Soare Название: Turing Computability ISBN: 3642319327 ISBN-13(EAN): 9783642319327 Издательство: Springer Рейтинг: Цена: 10480.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Centrone Stefania, Negri Sara, Sarikaya Deniz Название: Mathesis Universalis, Computability and Proof ISBN: 3030204499 ISBN-13(EAN): 9783030204495 Издательство: Springer Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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
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