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The Church-Turing Thesis

1. The Thesis and its History

❶This interpretation of the Church—Turing thesis differs from the interpretation commonly accepted in computability theory, discussed above. The first step of the Kripke argument is his claim that error-free, human computation is itself a form of deduction:.

2. Misunderstandings of the Thesis

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Computability and Complexity the Church-Turing Thesis: types of evidence • large sets of Turing-Computable functions many examples no counter-examples • equivalent to other formalisms for algorithms Church’s l calculus and others • intuitive - any detailed algorithm for manual calculation can be implemented by a Turing Machine.

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Quantum Computation and Extended Church-Turing Thesis Extended Church-Turing Thesis The extended Church-Turing thesis is a foundational principle in computer science.

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There are various equivalent formulations of the Church-Turing thesis. A common one is that every effective computation can be carried out by a Turing machine. The Church-Turing thesis is often misunderstood, particularly in recent writing in the philosophy of mind. The Church-Turing thesis in a quantum world Ashley Montanaro Centre for Quantum Information and Foundations, Department of Applied Mathematics and Theoretical Physics.

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In computability theory, the Church–Turing thesis (also known as computability thesis,[1] the Turing–Church thesis,[2] the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a hypothesis about the nature of computable functions. This PDF version matches the latest version of this entry. To view the PDF, you must Log In or Become a Member. You can also read more about the Friends of the SEP Society.