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Titlebook: New Computational Paradigms; Changing Conceptions S. Barry Cooper,Benedikt Löwe,Andrea Sorbi Book 2008 Springer-Verlag New York 2008 Analys

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发表于 2025-3-21 19:43:19 | 显示全部楼层 |阅读模式
书目名称New Computational Paradigms
副标题Changing Conceptions
编辑S. Barry Cooper,Benedikt Löwe,Andrea Sorbi
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概述Explores new developments in the theory and practice of computation from a mathematical perspective.Includes topics ranging from classical computability to complexity, biocomputing, and quantum comput
图书封面Titlebook: New Computational Paradigms; Changing Conceptions S. Barry Cooper,Benedikt Löwe,Andrea Sorbi Book 2008 Springer-Verlag New York 2008 Analys
描述.In recent years, classical computability has expanded beyond its original scope to address issues related to computability and complexity in algebra, analysis, and physics. The deep interconnection between "computation" and "proof" has originated much of the most significant work in constructive mathematics and mathematical logic of the last 70 years. Moreover, the increasingly compelling necessity to deal with computability in the real world (such as computing on continuous data, biological computing, and physical models) has brought focus to new paradigms of computation that are based on biological and physical models. These models address questions of efficiency in a radically new way and even threaten to move the so-called Turing barrier, i.e. the line between the decidable and the un-decidable...This book examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. The book opens with an introduction by Andrew Hodges, the Turing biographer, who analyzes the pioneering work that anticipated recent developments concerning computation’s
出版日期Book 2008
关键词Analysis; algorithms; complexity; complexity theory; computability theory; computer; computer science; info
版次1
doihttps://doi.org/10.1007/978-0-387-68546-5
isbn_softcover978-1-4419-2263-2
isbn_ebook978-0-387-68546-5
copyrightSpringer-Verlag New York 2008
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发表于 2025-3-22 00:06:23 | 显示全部楼层
Computation Paradigms in Light of Hilbert’s Tenth ProblemThis is a survey of a century-long history of interplay between Hilbert’s tenth problem (about solvability of Diophantine equations) and different notions and ideas from Computability Theory. The present paper is an extended version of [83].
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A Survey on Continuous Time ComputationsWe provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature.
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Applications of the Kleene–Kreisel Density Theorem to Theoretical Computer Scienceef introduction to the classic density theorem, then show how this may be generalized to set theoretical models for algorithms accepting real numbers as inputs, and finally survey some recent applications of this generalization.
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Metamathematical Properties of Intuitionistic Set Theories with Choice Principles several other metamathematical properties hold true for constructive Zermelo–Fraenkel Set Theory and full intuitionistic Zermelo–Fraenkel augmented by any combination of the principles of countable choice, dependent choices, and the presentation axiom. Also Markov’s principle may be added.
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https://doi.org/10.1007/978-0-387-68546-5Analysis; algorithms; complexity; complexity theory; computability theory; computer; computer science; info
发表于 2025-3-23 09:07:19 | 显示全部楼层
S. Barry Cooper,Benedikt Löwe,Andrea SorbiExplores new developments in the theory and practice of computation from a mathematical perspective.Includes topics ranging from classical computability to complexity, biocomputing, and quantum comput
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