[baddox]

That's a good point. The first sentence of the Wikipedia article says "Hypercomputation or super-Turing computation refers to models of computation that go beyond, or are incomparable to, Turing computability." The "incomparable to" part is sufficiently vague to shoehorn in asymptotic improvements if we want to. :)

Of course, an Zeno machine, or a machine that can solve the halting problem, could also certainly solve problems a TM can solve but asymptotically faster.

[dllthomas]

'The "incomparable to" part is sufficiently vague to shoehorn in asymptotic improvements if we want to.'

I totally agree, which is part of why the article didn't clear it up.

"Of course, an Zeno machine, or a machine that can solve the halting problem, could also certainly solve problems a TM can solve but asymptotically faster."

A Zeno machine, for sure. It is not immediately clear to me that this necessarily holds for anything that can solve the halting problem - what about a TM plus a halting problem oracle that would tell you in 2^(size of TM) whether a TM halts?

Of course the real question is whether asymptotically faster is enough to be "hypercomputation". Necessity is also interesting, but not the same thing.