Computation theory of cellular automata
Abstract
Selforganizing behaviour in cellular automata is discussed as a computational process. Formal language theory is used to extend dynamical systems theory descriptions of cellular automata. The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages. Many examples are given. The sizes of the minimal grammars for these languages provide measures of the complexities of the sets. This complexity is usually found to be nondecreasing with time. The limit sets generated by some classes of cellular automata correspond to regular languages. For other classes of cellular automata they appear to correspond to more complicated languages. Many properties of these sets are then formally noncomputable. It is suggested that such undecidability is common in these and other dynamical systems.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 March 1984
 DOI:
 10.1007/BF01217347
 Bibcode:
 1984CMaPh..96...15W