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Titlebook: Computability and Complexity; Foundations and Tool Rod Downey Textbook 2024 The Editor(s) (if applicable) and The Author(s), under exclusiv

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发表于 2025-3-21 16:46:27 | 显示全部楼层 |阅读模式
书目名称Computability and Complexity
副标题Foundations and Tool
编辑Rod Downey
视频video
概述Provides a uniquely concise introduction to these subjects.Includes numerous examples and exercises.Progresses from general to deeper models of computability
丛书名称Undergraduate Topics in Computer Science
图书封面Titlebook: Computability and Complexity; Foundations and Tool Rod Downey Textbook 2024 The Editor(s) (if applicable) and The Author(s), under exclusiv
描述.This is a book about computation, something which is ubiquitous in the modern world. More precisely, it examines computability theory and computational complexity theory. Computability theory is the part of mathematics and computer science which seeks to clarify what we mean by computation or algorithm. When is there a computational solution possible to some question? How can we show that none is possible? How computationally hard is the question we are concerned with? Arguably, this area lead to the development of digital computers. (Computational) complexity theory is an intellectual heir of computability theory. Complexity theory is concerned with understanding what resources are needed for computation, where typically we would measure the resources in terms of time and space. Can we perform some task in a feasible number of steps? Can we perform some algorithm with only a limited memory? Does randomness help? Are there standard approaches to overcoming computational difficulty?.
出版日期Textbook 2024
关键词Finite automata; NP-completeness; Parameterized complexity; Reducability; Recursion; Structural complexit
版次1
doihttps://doi.org/10.1007/978-3-031-53744-8
isbn_softcover978-3-031-53743-1
isbn_ebook978-3-031-53744-8Series ISSN 1863-7310 Series E-ISSN 2197-1781
issn_series 1863-7310
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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Undecidable Problemsion of the Collatz function, word problems in formal languages, the Entscheidungsproblem, word problems in semigroups and groups, and we finish with a proof of the undecidability of Hilbert’s 10th Problem for exponential Diophantine equations.
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Deeper Computabilityo deal with problems more complex than the halting problem, as delve more deeply into the fine structure of reducibilities and noncomputable sets. We introduce Turing reducibility. We prove the s-m-n theorem and recursion theorem. We will look at computable structure theory via computable linear ord
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Parameterized Complexityse methods for proving parameterized tractability and also give some basic results the completeness and hardness theory. We also look at limitations of the methods and XP-optimality. The latter gives methods for proving various algorithms are more or less optimal, subject to complexity consideration
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Textbook 2024al complexity theory. Computability theory is the part of mathematics and computer science which seeks to clarify what we mean by computation or algorithm. When is there a computational solution possible to some question? How can we show that none is possible? How computationally hard is the questio
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1863-7310 we would measure the resources in terms of time and space. Can we perform some task in a feasible number of steps? Can we perform some algorithm with only a limited memory? Does randomness help? Are there standard approaches to overcoming computational difficulty?.978-3-031-53743-1978-3-031-53744-8Series ISSN 1863-7310 Series E-ISSN 2197-1781
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