04198nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001700153072001600170072002300186072001500209100007400224245013600298250001800434264006900452300004700521336002600568337002600594338003600620347002400656490005700680505033900737520206701076650002203143650003003165650002603195650002203221650002603243650001903269650002703288650003003315650004003345650005103385650002103436710003403457773002603491776003603517776003603553830005703589856004603646978-3-031-53744-8DE-He21320251030112034.0cr nn 008mamaa240510s2024    sz |    s    |||| 0|eng d  a97830315374487 a10.1007/978-3-031-53744-82doi 4aQA75.5-76.95 7aUYA2bicssc 7aCOM0140002bisacsh 7aUYA2thema1 aDowney, Rod.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aComputability and Complexityh[electronic resource] :bFoundations and Tools for Pursuing Scientific Applications /cby Rod Downey.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXXVIII, 346 p. 17 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aUndergraduate Topics in Computer Science,x2197-17810 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.  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. 0aComputer science. 0aComputational complexity. 0aComputable functions. 0aRecursion theory. 0aApplication software. 0aSystem theory.14aTheory of Computation.24aComputational Complexity.24aComputability and Recursion Theory.24aComputer and Information Systems Applications.24aComplex Systems.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303153743108iPrinted edition:z9783031537455 0aUndergraduate Topics in Computer Science,x2197-178140uhttps://doi.org/10.1007/978-3-031-53744-8