Characterization of zigzag De Morgan functions

Abstract

Post’s functional completeness theorem for Boolean functions plays an important role in discrete mathematics. In paper [A functional completeness theorem for De Morgan functions, Discrete Appl. Math. 162 (2014) 1–16, doi: 10.1016/j.dam.2013.08.006.] a functional completeness criterion for De Morgan functions is established by the present author and Yu. Movsisyan. Namely, the concepts of closed, complete and precomplete classes of De Morgan functions are introduced there and a functional completeness theorem for De Morgan functions is proven. As a result it is shown that there are five precomplete classes of De Morgan functions. Four of those are defined as sets of functions preserving some finitary relations. However, the fifth class — the class of zigzag De Morgan functions, is not defined by relations. In this paper, we prove that zigzag De Morgan functions can be defined as De Morgan functions preserving an atmost 16-ary relation.