An Upper Bound on Checking Test Complexity for Almost All Cographs

Abstract

The concept of a checking test is of prime interest to the study of a variant of exact identification problem, in which the learner is given a hint about the unknown object. A graph F is said to be a checking test for a co graph G iff for any other co graph H there exists an edge in F distinguishing G and H, that is, contained in exactly one of the graphs G and H. It is known that for any co graph G there exists a unique irredundant checking test, the number of edges in which is called the checking test complexity of G. We show that almost all co graphs on n vertices have relatively small checking test complexity of O(n log n). Using this result, we obtain an upper bound on the checking test complexity of almost all read-once Boolean functions over the basis of disjunction and parity functions.