Oracle hypermachines faced with the verification problem

Florent Franchette

pp. 213-223

in: Gordana Dodig Crnkovic, Gordana Dodig-Crnkovic, Raffaela Giovagnoli (eds), Computing nature, Berlin, Springer, 2013

Abstract

One of the main current issues about hypercomputation concerns the claim of the possibility of building a physical device that hypercomputes. In order to prove this claim, one possible strategy could be to physically build an oracle hypermachine, namely a device which is be able to use some extern information from nature to go beyond Turing machines limits. However, there is an epistemological problem affecting this strategy, which may be called "verification problem". This problem raises in presence of an oracle hypermachine and it may be set out as follows: even if we were able to build such a hypermachine we would not be able to claim that it hypercomputes because it would be impossible to verify that the machine can compute a non Turing-computable function. In this paper, I propose an analysis of the verification problem in order to know whether it is a genuine problem for oracle hypermachines.