Interpolation by polynomial functions of distributive lattices: a generalization of a theorem of R. L. Goodstein
Waldhauser, Tamás; Couceiro, Miguel (2013), Interpolation by polynomial functions of distributive lattices: a generalization of a theorem of R. L. Goodstein, Algebra Universalis, 69, 3, p. 287-299. http://dx.doi.org/10.1007/s00012-013-0231-6
Type
Article accepté pour publication ou publiéExternal document link
http://arxiv.org/abs/1110.0321Date
2013Journal name
Algebra UniversalisVolume
69Number
3Publisher
Springer
Pages
287-299
Publication identifier
Metadata
Show full item recordAbstract (EN)
We consider the problem of interpolating functions partially defined over a distributive lattice, by means of lattice polynomial functions. Goodstein's theorem solves a particular instance of this interpolation problem on a distributive lattice L with least and greatest elements 0 and 1, resp.: Given an n-ary partial function f over L, defined on all 0-1 tuples, f can be extended to a lattice polynomial function p over L if and only if f is monotone; in this case, the interpolating polynomial p is unique. We extend Goodstein's theorem to a wider class of n-ary partial functions f over a distributive lattice L, not necessarily bounded, where the domain of f is a cuboid of the form D={a1,b1}x...x{an,bn} with aiSubjects / Keywords
Lattice polynomial function; distributive lattice; polynomial interpolation; Goodstein's theorem; disjunctive normal formRelated items
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