Proofs and Computations

This book PDF is perfect for those who love Mathematics genre, written by Helmut Schwichtenberg and published by Cambridge University Press which was released on 15 December 2011 with total hardcover pages 480. You could read this book directly on your devices with pdf, epub and kindle format, check detail and related Proofs and Computations books below.

Proofs and Computations
Proofs and Computations
Author : Helmut Schwichtenberg
File Size : 53,9 Mb
Publisher : Cambridge University Press
Language : English
Release Date : 15 December 2011
ISBN : 9781139504164
Pages : 480 pages
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Proofs and Computations by Helmut Schwichtenberg Book PDF Summary

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.

Proofs and Computations

Proofs and Computations by Helmut Schwichtenberg,Stanley S. Wainer

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 Gö

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Proof and Computation

Proof and Computation by Helmut Schwichtenberg

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.

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Proof and Computation

Proof and Computation by Klaus Mainzer,Helmut Schwichtenberg,Peter Schuster

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 Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. By

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Proof And Computation Digitization In Mathematics Computer Science And Philosophy

Proof And Computation Digitization In Mathematics Computer Science And Philosophy by Mainzer Klaus,Schwichtenberg Helmut,Schuster Peter Michael

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 Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. By

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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 by Klaus Mainzer,Helmut Schwichtenberg,Peter Michael Schuster

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

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Mathematics and Computation

Mathematics and Computation by Avi Wigderson

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

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Arithmetic Proof Theory and Computational Complexity

Arithmetic Proof Theory and Computational Complexity by Peter Clote,Jan Krajícek

This book principally concerns the rapidly growing area of "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory. Additional features of the book include (1) the transcription and translation of a recently discovered 1956 letter from K Godel to J

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Computational Complexity

Computational Complexity by Sanjeev Arora,Boaz Barak

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

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