The Arity Gap of Polynomial Functions over Bounded Distributive Lattices

Miguel Couceiro, Erkko Lehtonen
2010 2010 40th IEEE International Symposium on Multiple-Valued Logic  
Let A and B be arbitrary sets with at least two elements. The arity gap of a function f: A^n \to B is the minimum decrease in its essential arity when essential arguments of f are identified. In this paper we study the arity gap of polynomial functions over bounded distributive lattices and present a complete classification of such functions in terms of their arity gap. To this extent, we present a characterization of the essential arguments of polynomial functions, which we then use to show
more » ... t almost all lattice polynomial functions have arity gap 1, with the exception of truncated median functions, whose arity gap is 2.
doi:10.1109/ismvl.2010.29 dblp:conf/ismvl/CouceiroL10 fatcat:5ccf3jori5anxhjgadswadrksq