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9. What is the Church-Turing Thesis?

  • 2022
  • OriginalPaper
  • Chapter
Published in:
Authors
Udi Boker
Nachum Dershowitz
Published in
Axiomatic Thinking II
Publisher
Springer International Publishing

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Abstract

The Church-Turing Thesis is a foundational concept in computability theory, asserting that any function computable by an algorithm can be computed by a Turing machine, and vice versa. Originating from the work of Alonzo Church and Alan Turing in the 1930s, the thesis has been interpreted in various ways and debated extensively. The chapter delves into these interpretations, focusing on the extensional claim that all effective computations can be performed by Turing machines. It also examines the historical context, the philosophical arguments for and against the thesis, and the attempts to prove or disprove it. Notable arguments include Turing's convincing proof and Gödel's support for the thesis, as well as criticisms from Church, Kleene, and others. The chapter concludes by discussing the physical and mathematical theses and the implications of potential counterexamples to the Church-Turing Thesis. This detailed exploration offers readers a deep understanding of the thesis and its significance in the field of computability.
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[Answer:] Rosser and its inventor proved that its beta-reduction satisfies the diamond property, and Kleene (pron. clean-ee) proved that it was equivalent to his partial recursive functions. The previous result combined with a similar one with the Turing Machine, led to the Church-Turing thesis.
[Question: “What is ...?”]
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previous chapter Axiomatics as a Functional Strategy for Complex Proofs: The Case of Riemann Hypothesis
next chapter Axiomatic Thinking in Physics—Essence or Useless Ornament?
Title
What is the Church-Turing Thesis?
Authors
Udi Boker
Nachum Dershowitz
Copyright Year
2022
Book
Axiomatic Thinking II

Print ISBN: 978-3-030-77798-2

Electronic ISBN: 978-3-030-77799-9

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-030-77799-9_9
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