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We first introduce informally our grammatical scheme for modeling the generation or growth of data structures which can be viewed as the neighbor relations (topologically invariant) for planar maps, permitting binary division of "countries" or "cells", motivated by biological considerations and by the desire to generate successive patterns in the Lindenmayer fashion (i.e., by simultaneous...
The need for a measure different from the number of states in analyzing stochastic sequential machines is pointed out. Using the decomposition previously demonstrated in association with actual physical realization of stochastic sequential machines4, a particular measure of complexity C(M) for a given machine M is introduced. The computational aspect of C(M) is discussed and an example exhibiting...
The observer/state-calculable stochastic machine is such that the present state, input, and output determine the next state. It is shown that since, for such machines, an initial state leads to degenerate terminal distributions, and reduction by merging equivalent states leads to unique reduced forms, several interrelated difficulties in stochastic machine theory are suppressed when attention is restricted...
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