István Németi, Hajnal Andréka and Peter Németi (Budapest)
Relativistic Computing Beyond the Turing Barrier

By relativistic computing we mean general relativistic (GR) computing. As pointed out in earlier papers of the present authors, GR makes it possible to physically compute the "uncomputable" (at least in theory). In particular, we will show that we can design a physical experiment carrying out of which can tell the experimenter the answer to a Turing incomputable question. Such a question is, for example, deciding any recursive enumerable but not recursive set of the integers. We will claim that our future generations may be able to carry out such an experiment. In the talk we will discuss how and why. We will discuss various kinds of such relativistic hypercomputers. Among others, we will discuss hypercomputers based on kinds of Lorentzian wormholes, their connections with Einstein's equation and accelerating expansion of the Universe.