Recognition of tractable DNFs representable by a constant number of intervals

In this paper we focus on a less common way how to represent Boolean functions, namely on representations by intervals of truepoints and by switch-lists. There are two problems connected to such representation: (1) a knowledge compilation problem, i. e. a problem of transforming a given representation of a Boolean function (Boolean formula, binary decision diagram, Boolean circuit, …) into an interval or switch-list representation, and (2) a knowledge compression problem, i. e. a problem of finding the most compact interval or switch-list representation among those which represent the given function. We will summarize known results about these two problems and present generalizations in both areas. The main result is a polynomial time algorithm that for a Boolean function given by a tractable formula outputs a shortest interval and switch-list representations provided that the number of switches (intervals) is bounded by a constant. This algorithm can be also thought of as a polynomial time recognition algorithm for the class of k-switch (or k-interval) functions given by a tractable formula for any fixed k.