On the Complexity of Minimizing Quasicyclic Boolean Functions

Abstract

We investigate the Boolean functions that combine various properties: the extremal values of complexity characteristics ofminimization, the inapplicability of local methods for reducing the complexity of the exhaustion, and the impossibility to efficiently use sufficient minimality conditions. Some quasicyclic functions are constructed that possess the properties of cyclic and zone functions, the dominance of vertex sets, and the validity of sufficient minimality conditions based on independent families of sets. For such functions, we obtain the exponential lower bounds for the extent and special sets and also a twice exponential lower bound for the number of shortest and minimal complexes of faces with distinct sets of proper vertices.