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Questions tagged [church-turing-thesis]

For questions about the interpretation, extension and validity of the Church-Turing thesis, the hypothesis that states that a function is effectively calculable by a human if and only if the function is computable (on a Turing machine)

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Church-Turing Thesis and computational power of neural networks

The Church-Turing thesis states that everything that can physically be computed, can be computed on a Turing Machine. The paper "Analog computation via neural networks" (Siegelmannn and Sontag, Theoretical Computer Science, 131:331–360, 1994; PDF)…
John R. L
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Do any programming languages use general recursive functions as their basis?

This is a naïve and, therefore, possibly malformed question, so apologies in advance! My view is that a Turing Machine can be seen as the computational basis for procedural/imperative programming languages. Similarly, the lambda calculus is the…
Xophmeister
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Is there any uncountable Turing decidable language?

There are many(and I mean many) countable languages which are Turing-decidable. Can any uncountable language be Turing decidable?
Jyotirmoy Pramanik
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Turing machine + time dilation = solve the halting problem?

There are relativistic spacetimes (e.g. M-H spacetimes; see Hogarth 1994) where a worldline of infinite duration can be contained in the past of a finite observer. This means that a normal observer can have access to an infinite number of a…
K--
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Can every self-modifying algorithm be modelled by a non-selfmodifying algorithm?

If we have any arbitrary computer program that can modify its instructions, is it possible to simulate that program with a program that cannot modify its instructions? Edit: I am new to stackexchange so not sure if I'm allowed to ask a NEW question…
user56834
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Analog computers and the Church-Turing thesis

I'd like to quote from Nielsen & Chuang, Quantum Computation and Quantum Information, 10th anniversary edition, page 5 (emphasis mine): One class of challenges to the strong Church–Turing thesis comes from the field of analog computation. In the…
lionelbrits
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Clear, complete, proof that a language is Turing Compete?

I have seen web sites that purport to "prove" that HTML5+CSS is Turing Complete. I have seen web sites that purport to "prove" that SQL is Turing Complete. I have seen a bunch of web sites that purport to "explain" what it means to be Turing…
Roger Costello
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Why is Oracle Turing Machine important?

As you know, an Oracle Turing Machine (OTM) is a "black box" which somehow can tell us whether a given Turing machine with a given input eventually halts. By Church's Thesis it is impossible to design an algorithm which is able to solve such a…
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Church-Turing and physical PDEs

When I read about the Church-Turing thesis it seems to be a common claim that "physical reality is Turing-computable." What is the basis for this claim? Are there any theoretical results along these lines? For context, I am a researcher who works on…
user168715
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To what does typing correspond in a Turing Machine?

I hope my question makes sense: Starting with the premise that the untyped $\lambda $ calculus is equivalent in power to a Turing machine, to what in a Turing machine does adding types to the $\lambda $ calculus correspond? Is there some kind of…
BlueBomber
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Does this article imply that Turing-Computability is not the same as "effectively computable"?

I've stumbled across this article. It says that there is a problem that only Quantum Computers can solve. In my understanding, this should mean, intuitively, that this problem is "effectively computable", since we have an effective, real method to…
olinarr
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Does Church-Turing thesis also apply to artificial intelligence?

By Church-Turing's thesis, it is impossible to design an algorithm to decide the halting problem. Does the word algorithm in this context include artificial intelligence or not, that is, does Church-Turing thesis also apply to artificial…
M a m a D
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Does computability according to Church-Turing thesis include side effects?

To my understanding: The Church-Turing thesis means that one could theoretically compute anything that can be computed using either a Turing Machine or the Lambda Calculus. The Lambda Calculus is based on mathematical functions. This leads to…
dukereg
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Would creating a complete computer simulation of the human brain prove the Church-Turing thesis?

According to Wikipedia, the Church-Turing thesis "states that a function on the natural numbers is computable by a human being ignoring resource limitations if and only if it is computable by a Turing machine." If we made a complete simulation of…
Raiden Worley
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Is there an algorithm for converting Turing machines into equivalent Lambda expressions?

We know that Turing machines and Lambda Calculus are equivalent in power. And There are proofs for that, I'm sure. But is there an algorithm, a systematic way for us to convert a Turing machine into a Lambda Calculus expression? Is it impossible to…
Ashkan Kazemi
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