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020 _a9783031537448
_9978-3-031-53744-8
024 7 _a10.1007/978-3-031-53744-8
_2doi
050 4 _aQA75.5-76.95
072 7 _aUYA
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aUYA
_2thema
100 1 _aDowney, Rod.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_976603
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
_bPDF
_2rda
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.
_958552
650 0 _aComputational complexity.
650 0 _aComputable functions.
_976604
650 0 _aRecursion theory.
_976605
650 0 _aApplication software.
650 0 _aSystem theory.
_966519
650 1 4 _aTheory of Computation.
_967552
650 2 4 _aComputational Complexity.
650 2 4 _aComputability and Recursion Theory.
_976606
650 2 4 _aComputer and Information Systems Applications.
650 2 4 _aComplex Systems.
_966520
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031537431
776 0 8 _iPrinted edition:
_z9783031537455
830 0 _aUndergraduate Topics in Computer Science,
_x2197-1781
_966494
856 4 0 _uhttps://doi.org/10.1007/978-3-031-53744-8
912 _aZDB-2-SCS
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