Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array

Authors:
Shojiro Sakata
Affiliations:
Toyohashi University of Technology, Dept of Production Systems Engineering, Tempaku-cho, Toyohashi 440, Japan
Venue:
Journal of Symbolic Computation
Year:
1988

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Abstract

We present an algorithm for finding a minimal set of two-dimensional linear recurring relations capable of generating a prescribed finite two-dimensional array. This is a two-dimensional extension of the Berlekamp-Massey algorithm for synthesizing a shortest linear feedback shift-register capable of generating a given finite sequence. The complexity of computation for an array of size n is 0(n^2) under some reasonable assumptions. Furthermore, we make clear some relationship between our algorithm and Grobner bases of bivariate polynomial ideals, where polynomials correspond one-to-one to linear recurring relations.