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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.
The Stored-Program Universal Computer: Did Zuse Anticipate Turing and von Neumann?" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com
List of contents
Preface (Martin Davis).-I Introduction (Sommaruga, Strahm).-II Turing and the history of computability theory .- 1. Conceptual Confluence in 1936: Post & Turing, Martin Davis and Wilfried Sieg.- 2. Algorithms: From Al-Khwarizmi to Turing and Beyond, Wolfgang Thomas.- 3. The Stored-Program Universal Computer: Did Zuse Anticipate Turing and von Neumann? Jack Copeland and Giovanni Sommaruga.- III Generalizing Turing computability theory.- 1. Theses for Computation and Recursion on Concrete and Abstract Structures, Solomon Feferman.- 2. Generalizing Computability Theory to Abstract Algebras, John V. Tucker and Jeffrey Zucker.- 3. Discrete Transfinite Computation, Philip Welch.- 4. Semantics-to-Syntax Analyses of Algorithms, Yuri Gurevich.- 5. The Information Content of Typical Reals, George Barmpalias and Andy Lewis-Pye.- 6. Proof-theoretic Analysis by Iterated Reflection, Lev Beklemishev.-IV Philosophical reflections.- 1. Alan Turing and the Foundation of Computer Science, Juraj Hromkovic.- 2. Proving Things about the Informal, Stewart Shapiro.- 3. Why Turing's Thesis is Not a Thesis, Robert Soare.- 4. Incomputability, Emergent, and Higher Type Computation, S. Barry Cooper.
About the author
Giovanni Sommaruga is Professor for philosopy of logic and mathematics at ETH Zurich, Switzerland. Thomas Strahm is Professor for mathematical logic and theoretical computer science at the University of Berne, Switzerland.
Summary
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.
The Stored-Program Universal Computer: Did Zuse Anticipate Turing and von Neumann?” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com
Additional text
“There is a wide variety of content … in this collection about Turing’s ideas and what they meant for mathematics and computer science. … People of all mathematical and computer science backgrounds will find something of interest in this collection. Educators that would like to go deeper into the meaning of computability and algorithms can find material that will set the stage for discussions and research papers on the meaning and impact of the life and work of Alan Turing.” (Charles Ashbacher, MAA Reviews, maa.org, February, 2016)
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"There is a wide variety of content ... in this collection about Turing's ideas and what they meant for mathematics and computer science. ... People of all mathematical and computer science backgrounds will find something of interest in this collection. Educators that would like to go deeper into the meaning of computability and algorithms can find material that will set the stage for discussions and research papers on the meaning and impact of the life and work of Alan Turing." (Charles Ashbacher, MAA Reviews, maa.org, February, 2016)
