Computability

Tourlakis, George

  • 出版商: Springer
  • 出版日期: 2023-08-03
  • 售價: $2,940
  • 貴賓價: 9.5$2,793
  • 語言: 英文
  • 頁數: 637
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303083204X
  • ISBN-13: 9783030832049
  • 海外代購書籍(需單獨結帳)

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商品描述

This survey of computability theory offers the techniques and tools that computer scientists (as well as mathematicians and philosophers studying the mathematical foundations of computing) need to mathematically analyze computational processes and investigate the theoretical limitations of computing. Beginning with an introduction to the mathematisation of "mechanical process" using URM programs, this textbook explains basic theory such as primitive recursive functions and predicates and sequence-coding, partial recursive functions and predicates, and loop programs.

Advanced chapters cover the Ackerman function, Tarski's theorem on the non-representability of truth, Goedel's incompleteness and Rosser's incompleteness theorems, two short proofs of the incompleteness theorem that are based on Lob's deliverability conditions, Church's thesis, the second recursion theorem and applications, a provably recursive universal function for the primitive recursive functions, Oraclecomputations and various classes of computable functionals, the Arithmetical hierarchy, Turing reducibility and Turing degrees and the priority method, a thorough exposition of various versions of the first recursive theorem, Blum's complexity, Hierarchies of primitive recursive functions, and a machine-independent characterisation of Cobham's feasibly computable functions.

作者簡介

George Tourlakis, PHD, is University Professor of Computer Science and Engineering at York University in Toronto, Canada. He has published extensively in his areas of research interest, which include calculational logic, modal logic, computability, and complexity theory. Dr. Tourlakis is the author of Theory of Computation and Mathematical Logic, both published by Wiley, and Lectures in Logic and Set Theory; Volumes 1 and 2 (Cambridge University Press).

作者簡介(中文翻譯)

George Tourlakis博士是加拿大多倫多約克大學的計算機科學和工程學的大學教授。他在計算邏輯、模態邏輯、可計算性和複雜性理論等研究領域發表了大量的論文。Tourlakis博士是Wiley出版社的《計算理論》和《數學邏輯》的作者,也是劍橋大學出版社的《邏輯和集合論講義》第一卷和第二卷的作者。