LEADER 05044nam 22007095 450 001 9910726280003321 005 20230523143858.0 010 $a9783031269042$b(electronic bk.) 010 $z9783031269035 024 7 $a10.1007/978-3-031-26904-2 035 $a(MiAaPQ)EBC7253098 035 $a(Au-PeEL)EBL7253098 035 $a(OCoLC)1381711965 035 $a(DE-He213)978-3-031-26904-2 035 $a(PPN)270617094 035 $a(CKB)26773174400041 035 $a(EXLCZ)9926773174400041 100 $a20230523d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgorithms for Constructing Computably Enumerable Sets /$fby Kenneth J. Supowit 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (191 pages) 225 1 $aComputer Science Foundations and Applied Logic,$x2731-5762 311 08$aPrint version: Supowit, Kenneth J. Algorithms for Constructing Computably Enumerable Sets Cham : Springer International Publishing AG,c2023 9783031269035 320 $aIncludes bibliographical references. 327 $a1 Index of notation and terms -- 2 Set theory, requirements, witnesses -- 3 What?s new in this chapter? -- 4 Priorities (a splitting theorem) -- 5 Reductions, comparability (Kleene-Post Theorem) -- 6 Finite injury (Friedberg-Muchnik Theorem) -- 7 The Permanence Lemma -- 8 Permitting (Friedberg-Muchnik below C Theorem) -- 9 Length of agreement (Sacks Splitting Theorem) -- 10 Introduction to infinite injury -- 11 A tree of guesses (Weak Thickness Lemma) -- 12 An infinitely branching tree (Thickness Lemma) -- 13 True stages (another proof of the Thickness Lemma) -- 14 Joint custody (Minimal Pair Theorem) -- 15 Witness lists (Density Theorem) -- 16 The theme of this book: delaying tactics -- Appendix A: a pairing function -- Bibliograph -- Solutions to selected exercises. 330 $aLogicians have developed beautiful algorithmic techniques for the construction of computably enumerable sets. This textbook presents these techniques in a unified way that should appeal to computer scientists. Specifically, the book explains, organizes, and compares various algorithmic techniques used in computability theory (which was formerly called "classical recursion theory"). This area of study has produced some of the most beautiful and subtle algorithms ever developed for any problems. These algorithms are little-known outside of a niche within the mathematical logic community. By presenting them in a style familiar to computer scientists, the intent is to greatly broaden their influence and appeal. Topics and features: · All other books in this field focus on the mathematical results, rather than on the algorithms. · There are many exercises here, most of which relate to details of the algorithms. · The proofs involving priority trees are written here in greater detail, and with more intuition, than can be found elsewhere in the literature. · The algorithms are presented in a pseudocode very similar to that used in textbooks (such as that by Cormen, Leiserson, Rivest, and Stein) on concrete algorithms. · In addition to their aesthetic value, the algorithmic ideas developed for these abstract problems might find applications in more practical areas. Graduate students in computer science or in mathematical logic constitute the primary audience. Furthermore, when the author taught a one-semester graduate course based on this material, a number of advanced undergraduates, majoring in computer science or mathematics or both, took the course and flourished in it. Kenneth J. Supowit is an Associate Professor Emeritus, Department of Computer Science & Engineering, Ohio State University, Columbus, Ohio, US. 410 0$aComputer Science Foundations and Applied Logic,$x2731-5762 606 $aComputer science 606 $aComputable functions 606 $aRecursion theory 606 $aSet theory 606 $aComputer science?Mathematics 606 $aTheory of Computation 606 $aComputability and Recursion Theory 606 $aSet Theory 606 $aTheory and Algorithms for Application Domains 606 $aMathematics of Computing 615 0$aComputer science. 615 0$aComputable functions. 615 0$aRecursion theory. 615 0$aSet theory. 615 0$aComputer science?Mathematics. 615 14$aTheory of Computation. 615 24$aComputability and Recursion Theory. 615 24$aSet Theory. 615 24$aTheory and Algorithms for Application Domains. 615 24$aMathematics of Computing. 676 $a004.0151 676 $a004.0151 700 $aSupowit$b Kenneth J.$01359561 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910726280003321 996 $aAlgorithms for Constructing Computably Enumerable Sets$93374026 997 $aUNINA