Complexity Measures and Cellular
نویسندگان
چکیده
A bstract . Various observables meas urin g the complexi ty of an ensemble of pattern s are discussed , in par ticul ar statistical quantit ies rela ted to the convergence of block entropies, an d comp utation t heoret ical quanti ties related to a gram matical description of t he ensem ble. T hese measures of com plexity are applied to one-dime nsio nal cellular automata, by char acterizing the time evolution of the probability measure on configuration space in te rms of stochast ic finite automata. In particular it is found th at t he effective measure comp lexity increases linearly in time for an addit ive rule with a random initial state wit h density p ::j:. 1/2. Some results on t he convergence of block entropies for regular languages are shown, and context-free languages are also discussed. These results are used in an attempt to interpret the cri tical exponents observed by Grassberger in t he converge nce of block entropies for certain chaotic cellular automaton rules.
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