Unpredictability and Computational Irreducibility

TL;DR

This paper formalizes the concept of computational irreducibility, demonstrating that for such systems, predicting the nth state cannot be faster than simulating the entire process, with initial focus on cellular automata and general computable functions.

Contribution

It provides a robust formal definition of computational irreducibility applicable to cellular automata and general computable functions, linking irreducibility to the impossibility of shortcut computations.

Findings

Irreducible systems cannot be predicted faster than simulation.

Formal definition of computational irreducibility for cellular automata.

Extension of the concept to general computable functions.

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 nth step without having to follow the same path than simulating the automaton or the function", this implies genuinely, as intuitively expected, that if the behavior of an object is computationally irreducible, no computation of its nth state can be faster than the simulation itself.