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Questions tagged [hypercomputation]

For questions about models of computation that can compute functions that Turing machines cannot. Often, these models are able to solve the halting problem.

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Theoretical machines which are more powerful than Turing machines

Are there any theoretical machines which exceed Turing machines capability in at least some areas?
user1561358
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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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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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Do "Type-2" Turing machines with infinite length inputs have more computational power?

Certain idealizations of a Turing machine yield an increase in computational power, such as an inductive Turing machine, which can (trivially) solve the halting problem if it has an infinite amount of time to run. A related variation is the "type-2…
Mike Battaglia
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Computational power of Actor Model

In the question below, let TM be Turing machine, NTM be nondeterministic Turing machine and PTM be probabilistic Turing machine. In his paper "Actor Model of Computation: Scalable Robust Information Systems" Carl Hewitt proposes following…
Paul Sujkov
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Is there a formal way of defining a Zeno Machine?

The idea of a Zeno machine is pretty interesting to me, but I can't seem to find a formal definition for how a Zeno machine would work. I can find a couple of definitions around but they are all about the same (I suspect that everyone is cribbing…
Sriotchilism O'Zaic
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Can generalized Turing machines compute all reals?

Super-recursive algorithms are theoretical super-recursive algorithms are a generalization of ordinary algorithms that are more powerful, that is, compute more than Turing machines. In this entry it is said: A symbol sequence is computable in the…
sztorwi
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A paradox about cardinality of ALL and arithmetic hierarchies ― Did I just prove that ZFC is inconsistent?

This problem arose when I tried to find the arithmetic hierarchy that $\mathsf{ALL}$, the class of all formal languages over a finite alphabet, corresponds to (like how $\mathsf{R} = \Delta^0_1$ and $\mathsf{RE} = \Sigma^0_1$). Since the cardinality…
Dannyu NDos
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Can hypercomputation compute all kinds of incomputable numbers/functions/problems…etc?

Hypercomputation is a "cheat" that extends the capability of a Turing machine or quantum computer or cellular automaton by adding extra abilities. A standard method is "Oracle machines", Turing machines with an extra black box device that can be…
bautzeman
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Is infinitely fast computer fundamentally impossible even theoretically?

This may get slightly philosophical, but consider the following program: bool lampState = false; TimeSpan timeout = 1; while (true) { lampState = !lampState; Thread.Sleep(timeout); timeout = timeout / 2; } DotNet Fiddle link for C#…
Eiver
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Church-Turing thesis is a dualism

Church-Turing thesis : Every effectively calculable function is a TM-computable function. But, hypercomputation models are strictly more powerful than TM and can solve TM-uncomputable problems on the paper. Does this imply that, for one who believes…
François
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The Church-Turing thesis and Hyper-computation

I am not a computer scientist and this is my first question. This question is a question in layman terms and I also want the answer in layman terms. When I searched hyper-computation. There was a list of models of hyper-computers. Now, my question…
Rounak Sarkar
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Would any continuous model of the universe have/be based on hypercomputational laws?

I've read that when Turing-Church thesis is applied to the universe and physics, one of the three interpretations that we can use and is defended by some important physicists is that: "The universe is a hypercomputer and then it is possible to…
sztorwi
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Is Homomorphic Computation Possible Using Graph Theory

Homomorphic encryption allows to store data on a blockchain encrypted, but a smart contract is a program that is executed on a node on the blockchain, therefore the "source code" of the contract is not private; therefore it is desirable to build a…
Computer Scientist
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Is there a 4th barrier to computing?

I know there are three barriers of computation; the thermodynamic barrier, the light barrier and the quantum barrier. Let’s say we figure out how to send signals FTL, learn how to get rid of excess heat and continue down the ladder of nanotech,…
Max
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