General interpolation by polynomial functions of distributive lattices

Publication Type:
Conference Proceeding
Communications in Computer and Information Science, 2012, 299 CCIS (PART 3), pp. 347 - 355
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For a distributive lattice L, we consider the problem of interpolating functions f: D→L defined on a finite set DL n, by means of lattice polynomial functions of L. Two instances of this problem have already been solved. In the case when L is a distributive lattice with least and greatest elements 0 and 1, Goodstein proved that a function f: {0,1} n →L can be interpolated by a lattice polynomial function p: L n →L if and only if f is monotone; in this case, the interpolating polynomial p was shown to be unique. The interpolation problem was also considered in the more general setting where L is a distributive lattice, not necessarily bounded, and where DL n is allowed to range over cuboids with a i,b i L and a i
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