Decision lists and related Boolean functions

Abstract

We consider Boolean functions represented by decision lists, and study their relationships to other classes of Boolean functions. It turns out that the elementary class of 1­decision lists has interesting relationships to independently defined classes such as disguised Horn functions, readonce functions, nested differences of concepts, threshold functions, and 2­monotonic functions. In particular, 1­decision lists coincide with fragments of the mentioned classes. We further investigate the recognition problem for this class, as well as the extension problem in the context of partially defined Boolean functions (pdBfs). We show that finding an extension of a given pdBf in the class of 1­decision lists is possible in linear time. This improves on previous results. Moreover, we present an algorithm for enumerating all such extensions with polynomial delay.