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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 be the reasons for it? Was this area convincingly shown to be unpromising?

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3rd International Hypercomputation Workshop (HyperNet 11) – Marzio De Biasi Jan 1 '12 at 19:55
Thanks for this! – Velvet Ghost Jan 6 '12 at 13:31
Velvet Ghost asked: > is it true that the Bekenstein Bound refutes...? Well, there's a good case for that since it limits the information in a volume of space as a consequence of Murphy's Law. – user30490 Dec 25 '14 at 20:17
There weren't any black holes nearby to send a Turing machine into. – Andrej Bauer Dec 27 '14 at 0:00
up vote 18 down vote accepted

It would be better if you specified what you mean exactly by hyper-computation and gave evidence for why you think it has "died down".

In any case, assuming that you are talking about computation of functions over natural numbers (and finite strings) (since I think it is clear that models for higher type computation is a very active area, e.g. CCA) and models of computation not equivalent to computability defined by Turing machines, I don't think the claim is correct, for example see CiE'05 and CiE'11. Also see the criticisms made against the claim that hyper-computation is something new:

If you are interested, there is also some discussion on FOM mailing list starting by Timothy Chow's email about Martin Davis' article.

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Thanks a lot for that very informative reply. To be honest, my only acquaintance with hypercomputation is through Siegelmann's work on the computational power of neural nets back in the mid 1990's - and her proof that a particular neural net (the analog recurrent NN) is hypercomputational. The key to it's hypercomputational power is it's analog nature - it can have weights which are REAL numbers. So I was referring to the subfield of hypercomputation known as Real Computation. – Velvet Ghost Jan 6 '12 at 13:22
I had read Martin Davis' articles previously, and they were what started to make me think that hypercomputation was out of fashion. Btw... is it true that the Bekenstein Bound refutes any possibility of analog computation in this universe? – Velvet Ghost Jan 6 '12 at 13:32

There have been recent several conferences on the topic of infinitary computability, which have treated many topics in hypercomputation.

In addition, there have been special sessions on infinitary computability in many of the CiE conferences.

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Welcome to cstheory. – Kaveh Feb 28 '12 at 6:53
Thanks very much! – JDH Feb 28 '12 at 12:19

I don't think this is true. Searching Arxiv for papers on hypercomputation gets a bunch of hits.

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Hypercomputation refers to models of computation that are more powerful than Turing computability (see e.g. Wikipedia), whereas both, PostBQP=PP and P_CTC=PSPACE, are certainly computable. – Martin Schwarz Jan 1 '12 at 9:57
Ok I will edit my answer thanks. – Joshua Herman Jan 2 '12 at 7:11
I'm beginning to think that you're right, Joshua. Also, thanks for that link. – Velvet Ghost Jan 6 '12 at 13:14

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