From (Hanson and 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
- Hanson, James E., and James P. Crutchfield. April 15, 1997. "Computational Mechanics of Cellular Automata: An Example". Physica D: Nonlinear Phenomena, Lattice Dynamics, 103 (1):169–89. DOI.