Classification of Cellular Automata

  • Klaus SutnerEmail author
Reference work entry
Part of the Encyclopedia of Complexity and Systems Science Series book series (ECSSS)


Cellular automaton

For our purposes, a (one-dimensional) cellular automaton (CA) is given by a local map ρ : Σw → Σ where Σ is the underlying alphabet of the automaton and w is its width. As a data structure, suitable as input to a decision algorithm, a CA can thus be specified by a simple lookup table. We abuse notation and write ρ(x) for the result of applying the global map of the CA to configuration x ∈ Σ.

Finite configurations

One often considers CA with a special quiescent state: the homogeneous configuration where all cells are in the quiescent state is required to be fixed point under the global map. Infinite configurations where all but finitely many cells are in the quiescent state are often called finite configurations. This is somewhat of a misnomer; we prefer to speak about configurations with finite support.


A discrete dynamical system is reversible if the evolution of the system incurs no loss of information: the state at time tcan be recovered...


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA

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