Abstract
The paper presents an exploration of conceptual issues that have arisen in the course of investigating speed-up and slowdown phenomena in small Turing machines, in particular results of a test that may spur experimental approaches to the notion of computational irreducibility. The test involves a systematic attempt to outrun the computation of a large number of small Turing machines (3 and 4 state, 2 symbol) by means of integer sequence prediction using a specialized function for that purpose. The experiment prompts an investigation into rates of convergence of decision procedures and the decidability of sets in addition to a discussion of the (un)predictability of deterministic computing systems in practice. We think this investigation constitutes a novel approach to the discussion of an epistemological question in the context of a computer simulation, and thus represents an interesting exploration at the boundary between philosophical concerns and computational experiments.
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Zenil, H., Soler-Toscano, F. & Joosten, J.J. Empirical Encounters with Computational Irreducibility and Unpredictability. Minds & Machines 22, 149–165 (2012). https://doi.org/10.1007/s11023-011-9262-y
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DOI: https://doi.org/10.1007/s11023-011-9262-y