Abstract
The intention of this talk is to look at various models of transfinite computation and give some calculations as to their comparative power. To clarify the kind of models that we are looking at, they will all be discrete acting: this will mean that they essentially perform simple discrete tasks in simple steps or stages. The reader should have in mind the paradigm of the standard Turing Machine which of course performs such simple actions as moving one cell left or right on the tape that it is reading, altering a symbol, changing a state etc etc. We are thus not considering any kind of machine or notional device that computes in an analogue fashion, nor any machine, such as neural network with nodes primed by infinitely precise real numbers, nor computations performed in chemistry beakers, across cell membranes, or in buckets of slime.
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Welch, P.D.: Turing Unbound: The extent of computations in Malament-Hogarth spacetimes. British Journal for Philosophy of Science (submitted)
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Welch, P.D. (2007). Turing Unbound: Transfinite Computation. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_82
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