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Universalities in Cellular Automata*

  • Nicolas Ollinger

Abstract

This chapter is dedicated to computational universalities in cellular automata, essentially Turing universality, the ability to compute any recursive function, and intrinsic universality, the ability to simulate any other cellular automaton. Constructions of Boolean circuits simulation in the two-dimensional case are explained in detail to achieve both kinds of universality. A detailed chronology of seminal papers is given, followed by a brief discussion of the formalization of universalities. The more difficult one-dimensional case is then discussed. Seminal universal cellular automata and encoding techniques are presented in both dimensions.

Keywords

Boolean Function Cellular Automaton Turing Machine Finite State Machine Boolean Circuit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgment

The author would like to thank G. Richard for providing and preparing figures to illustrate both rule 110 and the 4-state intrinsically universal cellular automaton.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Nicolas Ollinger
    • 1
  1. 1.Laboratoire d'informatique fondamentale de Marseille (LIF)Aix-Marseille Université, CNRSMarseilleFrance

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