Testing Monotone Read-Once Functions

A checking test for a monotone read-once function f depending essentially on all its n variables is a set of vectors M distinguishing f from all other monotone read-once functions of the same variables. We describe an inductive procedure for obtaining individual lower and upper bounds on the minimal number of vectors T (f) in a checking test for any function f . The task of deriving the exact value of T (f) is reduced to a combinatorial optimization problem related to graph connectivity. We show that for almost all functions f expressible by read-once conjunctive or disjunctive normal forms, T (f) ∼ n/ ln n. For several classes of functions our results give the exact value of T (f).