Unpredictability and Computational Irreducibility

  • Hervé Zwirn
  • Jean-Paul Delahaye
Part of the Emergence, Complexity and Computation book series (ECC, volume 2)


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.


Complexity logical depth cellular automata irreducibility computation 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.UFR de Physique (Université Paris 7), and CMLA (ENS Cachan) & IHPST (CNRS)ParisFrance
  2. 2.Laboratoire d’Informatique Fondamentale de Lille (CNRS)LilleFrance

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