Abstract
AbstractRealization theory for non‐linear systems is now quite firmly established. As an application of the theory a problem in figure realization, representing a new kind of realization problem, is considered. The problem is to find the necessary and sufficient system of rules for reconstructing a given figure (two‐dimensional array). The commutative linear representation system is considered to provide the set of rules for generating the figure. The array realization theorem can be stated as follows. For any given array there exist at least two canonical commutative linear representation systems which realize the array, and any two canonical commutative linear representation systems are isomorphic. Circumstances requiring computer treatment of figures are becoming more frequent. The theory of array realization presented in this paper can serve as a basis for figure coding theory. Examples are given of the behavior (figures) of one‐dimensional and two‐dimensional commutative linear representation systems, and the relation between the commutative linear representation system and the two‐dimensional system is discussed.
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