The Foundations of Computability Theory

The book provides an original and informative view of the development of computability theory, emphasizing its historical context and logical and formal development. It covers classical computability theory, relative computability, and the computability (Church-Turing) thesis, and includes a glossary, bibliographic references, and new sections. It is valuable as a textbook and guide for advanced undergraduate and graduate students and researchers in computability theory and theoretical computer science.

Format: Paperback / softback
Length: 422 pages
Publication date: 14 November 2021
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

This book provides a unique and insightful perspective on the evolution of fundamental concepts in computability theory. It contextualizes these ideas within their historical context, highlighting both the motivations behind them and the rigorous logical and formal development processes. In Part I, the author introduces computability theory, delving into the foundational crisis of mathematics in the early twentieth century and the emergence of formalism. In Part II, the author explores classical computability theory, discussing the quest for formalization, the Turing Machine, and notable achievements such as defining incomputable problems, such as computably enumerable sets, and developing methods for proving their incomputability. In Part III, the author delves into relative computability, covering topics such as computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, and the priority method. Finally, in Part IV, the author revisits the computability (Church-Turing) thesis in greater detail, offering a systematic and comprehensive account of its origins, evolution, and significance. He also discusses more powerful modern versions of the thesis and explores recent speculative proposals for new computing paradigms, such as hypercomputing.

This book serves as a valuable textbook and reference for advanced undergraduate and graduate students, as well as researchers in computability theory and theoretical computer science. The new edition of this book has been extensively revised, with nearly one hundred pages of new material. Notably, the author has adopted more contemporary and consistent terminology, addressing any notational redundancies and minor errors.

Overall, this book offers a comprehensive and accessible introduction to computability theory, making it an essential resource for anyone interested in this field.

Weight: 676g
Dimension: 235 x 155 (mm)
ISBN-13: 9783662624234
Edition number: 2nd ed. 2020