Multi-state Canalyzing Functions over Finite Fields

Abstract

In this paper, we extend the definition of Boolean canalyzing functions to the canalyzing functions over finite field ${\mathbb{F}}_q$, where $q$ is a power of a prime. We obtain the characterization of all the eight classes of such functions as well as their cardinality. When $q=2$, we obtain a combinatorial identity by equating our result to the formula in \cite{Win}. Finally, for a better understanding to the magnitude, we obtain the asymptotes for all the eight cardinalities as either $n\to \infty$ or $q\to \infty$.

References in corpus (1)

• Random Boolean Network Models and the Yeast Transcriptional Network

Cited by in corpus (1)

• Boolean nested canalizing functions: a comprehensive analysis