Functions Computed by Monotone Boolean Formulas with no Repeated Variables

Abstract If g is a monotone boolean function depending on all its variables, the property that each prime implicant of g intersects each prime clause of g in a singleton is a well-known necessary condition for g to be computable by a formula with no repeated variable, and only using the connectives and , or . We prove that the condition is also sufficient. Our proof uses matroid theory.