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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Is there any model of Game of Life compatible with hypercomputation?

I found a question in Mathematics Stack Exchange which asks a very similar question (https://math.stackexchange.com/questions/1023812/hypercomputation-higher-dimensional-variants-of-conways-game-of-...
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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 ...
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Can we see all of mathematics as an attempt to simplify computations?

This is a rather strong claim, and therefore likely to be incorrect, but hear me out. Firstly, when I talk of “computations”, I mean this in a broader sense than normally used, because I am including ...
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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 ...
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Would Schmidhuber's theories of everything be capable of performing hypercomputation?

Jürgen Schmidhuber pointed out that a simple explanation of the universe would be a Turing machine analogy programmed to execute all possible programs computing all possible histories for all types of ...
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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 ...
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Church-Turing thesis and hypercomputation?

The Church-Turing is a hypothesis about the nature of computable functions. It states that a function on the natural numbers is computable by a human being following an algorithm, ignoring resource ...
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1answer
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Would hypercomputation machines be capable of simulating/computing/programming everything?

If uncomputable numbers existed, could this hypercomputation machines compute them? Could hypercomputation compute all types of uncomputable things? Even truly inconsistent things? Even things that ...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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Is infinitely fast computer fundamentally impossible even theoretically?

This may get slightly philosophical, but consider the following program: ...
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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 ...