Turing`s Revolution: The Impact of His Ideas about Computability, Sommaruga Giovanni, Strahm Thomas
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: Stefania Centrone; Sara Negri; Deniz Sarikaya; Pet Название: Mathesis Universalis, Computability and Proof ISBN: 3030204464 ISBN-13(EAN): 9783030204464 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis […] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever.In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gr?nde”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory.The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
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: Rogers, H. Название: Theory of recursive functions and effective computability / ISBN: 0262680521 ISBN-13(EAN): 9780262680523 Издательство: MIT Press Рейтинг: Цена: 8465.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: (Reprint of the 1967 edition)
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.
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: Soare Robert I. Название: Turing Computability: Theory and Applications ISBN: 3662568586 ISBN-13(EAN): 9783662568583 Издательство: Springer Рейтинг: Цена: 7965.00 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: Nourani Название: Algebraic Computability and Enumeration Models ISBN: 1771882476 ISBN-13(EAN): 9781771882477 Издательство: Taylor&Francis Рейтинг: Цена: 21437.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements.
Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic types of models. New homotopy techniques are applied to Marin Lof types of computations with model categories. Functorial computability, induction, and recursion are examined in view of the above, presenting new computability techniques with monad transformations and projective sets.
This informative volume will give readers a complete new feel for models, computability, recursion sets, complexity, and realizability. This book pulls together functorial thoughts, models, computability, sets, recursion, arithmetic hierarchy, filters, with real tree computing areas, presented in a very intuitive manner for university teaching, with exercises for every chapter. The book will also prove valuable for faculty in computer science and mathematics.
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.
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: 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: 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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