Turing Computability: Theory and Applications, Soare Robert I.
Автор: Soare Название: Turing Computability ISBN: 3642319327 ISBN-13(EAN): 9783642319327 Издательство: Springer Рейтинг: Цена: 69870.00 T 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: 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: 111790.00 T 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: Nourani Название: Algebraic Computability and Enumeration Models ISBN: 1771882476 ISBN-13(EAN): 9781771882477 Издательство: Taylor&Francis Рейтинг: Цена: 142910.00 T 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: Pippenger Название: Theories of Computability ISBN: 0521553806 ISBN-13(EAN): 9780521553803 Издательство: Cambridge Academ Рейтинг: Цена: 98210.00 T 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: C.S. Calude; M.J. Dinneen; S. Sburlan Название: Combinatorics, Computability and Logic ISBN: 1852335262 ISBN-13(EAN): 9781852335267 Издательство: Springer Рейтинг: Цена: 121110.00 T 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: Rogers, H. Название: Theory of recursive functions and effective computability / ISBN: 0262680521 ISBN-13(EAN): 9780262680523 Издательство: MIT Press Рейтинг: Цена: 56430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: (Reprint of the 1967 edition)
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 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: George S. Boolos Название: Computability and logic ISBN: 0521701465 ISBN-13(EAN): 9780521701464 Издательство: Cambridge Academ Рейтинг: Цена: 33790.00 T 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: Eugenio G. Omodeo; Alberto Policriti Название: Martin Davis on Computability, Computational Logic, and Mathematical Foundations ISBN: 3319418416 ISBN-13(EAN): 9783319418414 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. 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: Rebecca Weber Название: Computability Theory ISBN: 082187392X ISBN-13(EAN): 9780821873922 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 36960.00 T Наличие на складе: Невозможна поставка. 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: Olinick Michael Название: Simply Turing ISBN: 1943657378 ISBN-13(EAN): 9781943657377 Издательство: Неизвестно Рейтинг: Цена: 7750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Alan Turing`s (1912-1954) belief that computers would one day be able to learn has not yet been proven, but this English mathematician, logician, and code breaker was a pioneer in the field of computer science and artificial intelligence.
Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years. The field has developed growing connections in diverse areas of mathematics, with applications suitable to topology, group theory, and other subfields.
In A Hierarchy of Turing Degrees, Rod Downey and Noam Greenberg introduce a new hierarchy that allows them to classify the combinatorics of constructions from many areas of computability theory, including algorithmic randomness, Turing degrees, effectively closed sets, and effective structure theory. This unifying hierarchy gives rise to new natural definability results for Turing degree classes, demonstrating how dynamic constructions become reflected in definability. Downey and Greenberg present numerous construction techniques involving high-level nonuniform arguments, and their self-contained work is appropriate for graduate students and researchers.
Blending traditional and modern research results in computability theory, A Hierarchy of Turing Degrees establishes novel directions in the field.
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