Abstract
Classical models of computation no longer fully correspond to the current notions of computing in modern systems. Even in the sciences, many natural systems are now viewed as systems that compute. Can one devise models of computation that capture the notion of computing as seen today and that could play the same role as Turing machines did for the classical case? We propose two models inspired from key mechanisms of current systems in both artificial and natural environments: evolving automata and interactive Turing machines with advice. The two models represent relevant adjustments in our apprehension of computing: the shift to potentially non-terminating interactive computations, the shift towards systems whose hardware and/or software can change over time, and the shift to computing systems that evolve in an unpredictable, non-uniform way. The two models are shown to be equivalent and both are provably computationally more powerful than the models covered by the old computing paradigm. The models also motivate the extension of classical complexity theory by non-uniform classes, using the computational resources that are natural to these models. Of course, the additional computational power of the models cannot in general be meaningfully exploited in concrete goal-oriented computations.
This research was partially supported by project BRICKS in the Netherlands, and by Institutional Research Plan AV0Z10300504 and grants No. 1ET100300419 and 1ET100300517 within the Czech National Research Program ‘Information Society’.
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Wiedermann, J., van Leeuwen, J. (2008). How We Think of Computing Today. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_61
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DOI: https://doi.org/10.1007/978-3-540-69407-6_61
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