An Introduction to post-Newtonian and non- Turing computation
Mike Stannett · 2000
In our paper [Sta90], we described a model of computation ‐ the Analog X-Machine ‐ with arguably ‘super-Turing’ computational power. Subsequent work has been reported, both at a seminar held at Sussex University, and via the Connectionists electronic bulletin board. Following enquiries from some twenty sites world-wide, it is clear that, although much interest exists in this general area, few researchers are aware of existing results. Indeed, some have expressed surprise that ‘non-Turing computation’ could be a meaningful concept in the first place. In this paper, accordingly, we set out those few results which we have managed to trace in the literature, together with our own recent thoughts, and identify possible areas of interest over the next few years. We have tried throughout to write with the technical non-specialist in mind; where appropriate, the more theoretically minded reader should consult the references for detailed proofs. A few technical details have been embedded in the text in the form of notes.