The Number of Canalyzing Functions over Any Finite Set

Abstract

In this paper, we extend the definition of Boolean canalyzing functions to the canalyzing functions of multi-state case. Namely, f:Q n → Q , where Q={a 1 ,a 2 ,...,a q } . We obtain its cardinality and the cardinalities of its various subsets (They may not be disjoint). When q= 2 , we obtain a combinatorial identity by equating our result to the formula in [1]. For a better understanding to the magnitude, we obtain the asymptotes for all the cardinalities as either n → ∞ or q → ∞ .