Abstract
We explore several concepts for analyzing the intuitive notion of computational irreducibility and we propose a robust formal definition, first in the field of cellular automata and then in the general field of any computable function f from N to N. We prove that, through a robust definition of what means “to be unable to compute the n th step without having to follow the same path than simulating the automaton or to be unable to compute f(n) without having to compute f(i) for i = 1 to n–1”, this implies genuinely, as intuitively expected, that if the behavior of an object is computationally irreducible, no computation of its n th state can be faster than the simulation itself.
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Zwirn, H., Delahaye, JP. (2013). Unpredictability and Computational Irreducibility. In: Zenil, H. (eds) Irreducibility and Computational Equivalence. Emergence, Complexity and Computation, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35482-3_19
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DOI: https://doi.org/10.1007/978-3-642-35482-3_19
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