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Does hyper-computational power of infinite time Turing machines also require infinite memory?

Can a infinite time Turing machine perform hyper-computation like checking the consistency of the set theory ZF without using infinite memory?
Inducto's user avatar
  • 27
19 votes
3 answers
2k views

Why has hypercomputation research died down?

I see a lot of research on hypercomputation in the 1990's, but in more recent years there seems to be little work on the topic. Is it true that research in this area has died down? If so, what could ...
Velvet Ghost's user avatar
20 votes
3 answers
3k views

How do models of hypercomputation overcome the Halting Problem?

Hypercomputation refers to models of computation that are not possible to simulate using Turing machines. (Hypercomputers are not necessarily physically realisable!) Some hypercomputers have access ...
András Salamon's user avatar
97 votes
10 answers
21k views

What would it mean to disprove Church-Turing thesis?

Sorry for the catchy title. I want to understand, what should one have to do to disprove the Church-Turing thesis? Somewhere I read it's mathematically impossible to do it! Why? Turing, Rosser etc ...
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