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downey r computability complexity foundations tools 2024

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Textbook in PDF format 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? From the Preface: The goal of this book is to give a straightforward introduction to the main ideas in these areas, at least from my own biased point of view. The book has been derived from various courses I have taught at Victoria University of Wellington, University of Madison, Wisconsin, Notre Dame, University of Chicago, Cornell University, Nanyang University of Technology, and elsewhere over the last 35 years. The target audience is somewhere around advanced undergraduate and beginning graduate students. This text could be also used by a professional mathematician to gain a thorough grounding in computability and computational complexity. The topics covered include basic naive set theory, regular languages and automata, models of computation, undecidability proofs, classical computability theory including the arithmetical hierarchy and the priority method, the basics of computational complexity, hierarchy theorems, NP and PSPACE completeness, structural complexity such as Oracle results, parameterized complexity and other methods of coping such as approximation, average case complexity, generic case complexity and smoothed analysis. Part I Background 1 Some Naive Set Theory Part II Computability Theory 2 Regular Languages and Finite Automata 3 General Models of Computation 4 Undecidable Problems 5 Deeper Computability Part III Computational Complexity Theory 6 Computational Complexity 7 NP- and PSPACE-Completeness 8 Some Structural Complexity 9 Parameterized Complexity 10 Other Approaches to Coping with Hardness Part IV Selected Solutions to Exercises 11 Solutions

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Downey R. Computability and Complexity. Foundations and Tools...2024.pdf 3.8 MB

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downey r computability complexity foundations tools 2024

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