We investigate the minor order of functions, focusing on upper covers and common upper bounds of pairs of functions. We show that two functions of arities m and n have a common upper bound if and only if they have a common lower bound, and if a common upper bound exists, then there is one of arity m + n − 1. Moreover, we determine the possible essential arities of upper covers of functions.
|Number of pages||14|
|Publication status||Published - 1 Jul 2018|
- Boolean function, Essential arity, Function of several arguments, Minor order, Upper cover