149 research outputs found
The arity gap of polynomial functions over bounded distributive lattices
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 that almost all lattice polynomial
functions have arity gap 1, with the exception of truncated median functions,
whose arity gap is 2.Comment: 7 page
Additive decomposability of functions over abelian groups
Abelian groups are classified by the existence of certain additive
decompositions of group-valued functions of several variables with arity gap 2.Comment: 17 page
Linearly definable classes of Boolean functions
International audienceIn this paper we address the question "How many properties of Boolean functions can be defined by means of linear equations?" It follows from a result by Sparks that there are countably many such linearly definable classes of Boolean functions. In this paper, we refine this result by completely describing these classes. This work is tightly related with the theory of function minors and stable classes, a topic that has been widely investigated in recent years by several authors including Maurice Pouzet
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