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024 7 _a10.1007/978-3-031-53744-8
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082 0 4 _a004.0151
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100 1 _aDowney, Rod.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_9101657
245 1 0 _aComputability and Complexity
_h[electronic resource] :
_bFoundations and Tools for Pursuing Scientific Applications /
_cby Rod Downey.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXXVIII, 346 p. 17 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
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490 1 _aUndergraduate Topics in Computer Science,
_x2197-1781
505 0 _aIntroduction -- Some Naive Set Theory -- Regular Languages and Finite Automata -- General Models of Computation -- Deeper Computability -- Computational Complexity -- NP- and PSPACE-Completeness -- Some Structural Complexity -- Parameterized Complexity -- Average Case, Smoothed Analysis, and Generic Case -- Complexity -- References.
520 _aThe ideas and techniques comprised in the mathematical framework for understanding computation should form part of the standard background of a graduate in mathematics or computer science, as the issues of computability and complexity permeate modern science. This textbook/reference offers a straightforward and thorough grounding in the theory of computability and computational complexity. Among topics covered are basic naive set theory, regular languages and automata, models of computation, partial recursive functions, undecidability proofs, classical computability theory including the arithmetical hierarchy and the priority method, the basics of computational complexity and hierarchy theorems. Topics and features: · Explores Conway's undecidability proof of the ``3x+1'' problem using reductions from Register Machines and "Fractran" · Offers an accessible account of the undecidability of the exponential version of Hilbert's 10th problem due to Jones and Matijacevič · Provides basic material on computable structure, such as computable linear orderings · Addresses parameterized complexity theory, including applications to algorithmic lower bounds and kernelization lower bounds · Delivers a short account of generic-case complexity and of smoothed analysis · Includes bonus material on structural complexity theory and priority arguments in computability theory This comprehensive textbook will be ideal for advanced undergraduates or beginning graduates, preparing them well for more advanced studies or applications in science. Additionally, it could serve such needs for mathematicians or for scientists working in computational areas, such as biology. Rodney Downey is an Emeritus Professor at Victoria University of Wellington, NZ. He is the co-author of the Springer books, Fundamentals of Parameterized Complexity, and Algorithmic Randomness and Complexity. He has won many prizes for his work, including (twice) the Shoenfield Prize for writing, as well as the Rutherford Medal, New Zealand's premier science award.
650 0 _aComputer science.
_99832
650 0 _aComputational complexity.
_93729
650 0 _aComputable functions.
_965525
650 0 _aRecursion theory.
_9101659
650 0 _aApplication software.
_9101660
650 0 _aSystem theory.
_93409
650 1 4 _aTheory of Computation.
_9101662
650 2 4 _aComputational Complexity.
_93729
650 2 4 _aComputability and Recursion Theory.
_9101663
650 2 4 _aComputer and Information Systems Applications.
_9101665
650 2 4 _aComplex Systems.
_918136
710 2 _aSpringerLink (Online service)
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773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
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776 0 8 _iPrinted edition:
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830 0 _aUndergraduate Topics in Computer Science,
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856 4 0 _uhttps://doi.org/10.1007/978-3-031-53744-8
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