Proofs and Computations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proofs and Computations write by Helmut Schwichtenberg. This book was released on 2011-12-15. Proofs and Computations available in PDF, EPUB and Kindle. Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
Mathematics and Computation
Mathematics and Computation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematics and Computation write by Avi Wigderson. This book was released on 2019-10-29. Mathematics and Computation available in PDF, EPUB and Kindle. An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Proof and Computation
Proof and Computation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proof and Computation write by Helmut Schwichtenberg. This book was released on 2012-12-06. Proof and Computation available in PDF, EPUB and Kindle. Logical concepts and methods are of growing importance in many areas of computer science. The proofs-as-programs paradigm and the wide acceptance of Prolog show this clearly. The logical notion of a formal proof in various constructive systems can be viewed as a very explicit way to describe a computation procedure. Also conversely, the development of logical systems has been influenced by accumulating knowledge on rewriting and unification techniques. This volume contains a series of lectures by leading researchers giving a presentation of new ideas on the impact of the concept of a formal proof on computation theory. The subjects covered are: specification and abstract data types, proving techniques, constructive methods, linear logic, and concurrency and logic.
Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification
Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification write by Klaus Mainzer. This book was released on 2021-07-27. Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification available in PDF, EPUB and Kindle. This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Computational Complexity
Computational Complexity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Complexity write by Sanjeev Arora. This book was released on 2009-04-20. Computational Complexity available in PDF, EPUB and Kindle. New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
