# Cellular automata as regular languages

tags
Cellular automata, Finite state machines

From (Hanson, Crutchfield 1997):

Finite state machines are appropriate for investigating pattern dynamics of CAs for a number of reasons, among which we may note the following:

• FAs encompass the full range of behavior types from periodic to complex to random;
• Characterization of patterns using FAs makes possible a definition of pattern complexity which is both natural and computable in practice;
• Ensemble evolution in the space of regular languages is closed under the CA rule;
• The CA update rule is itself an FST;
• Automated inference techniques exist for reconstructing FAs from experimental data

## Bibliography

1. . . "Computational Mechanics of Cellular Automata: An Example". Physica D: Nonlinear Phenomena, Lattice Dynamics, 103 (1):169–89. DOI.

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