Abstract
We introduce a generalization of Blum-Shub-Smale machines on the standard real numbers ℝ that is allowed to run for a transfinite ordinal number of steps before terminating. At limit times, register contents are set to the ordinary limit of previous register contents in ℝ. It is shown that each such machine halts before time ω ω or diverges. We undertake first steps towards estimating the computational strength of these new machines.
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Koepke, P., Seyfferth, B. (2012). Towards a Theory of Infinite Time Blum-Shub-Smale Machines. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_41
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DOI: https://doi.org/10.1007/978-3-642-30870-3_41
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