This book provides an overview of the confluence of ideas in Turing’s era and work and examines the impact of his work on mathematical logic and theoretical computer science. It combines contributions by well-known scientists on the history and philosophy of computability theory as well as on generalised Turing computability. By looking at the roots and at the philosophical and technical influence of Turing’s work, it is possible to gather new perspectives and new research topics which might be considered as a continuation of Turing’s working ideas well into the 21st century.
Author(s): Giovanni Sommaruga, Thomas Strahm (eds.)
Edition: 1
Publisher: Birkhäuser
Year: 2016
Language: English
Pages: 327
Tags: Mathematical Logic and Foundations; History of Mathematical Sciences; Logic
Front Matter....Pages i-xxiv
Front Matter....Pages 1-1
Conceptual Confluence in 1936: Post and Turing....Pages 3-27
Algorithms: From Al-Khwarizmi to Turing and Beyond....Pages 29-42
The Stored-Program Universal Computer: Did Zuse Anticipate Turing and von Neumann?....Pages 43-101
Front Matter....Pages 103-103
Theses for Computation and Recursion on Concrete and Abstract Structures....Pages 105-126
Generalizing Computability Theory to Abstract Algebras....Pages 127-160
Discrete Transfinite Computation....Pages 161-185
Semantics-to-Syntax Analyses of Algorithms....Pages 187-206
The Information Content of Typical Reals....Pages 207-224
Proof Theoretic Analysis by Iterated Reflection....Pages 225-270
Front Matter....Pages 271-271
Alan Turing and the Foundation of Computer Science....Pages 273-281
Proving Things About the Informal....Pages 283-296
Why Turing’s Thesis Is Not a Thesis....Pages 297-310
Incomputability Emergent, and Higher Type Computation....Pages 311-329
