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Recognition of tractable DNFs representable by a constant number of intervals

Publikace na Matematicko-fyzikální fakulta |
2017

Tento text není v aktuálním jazyce dostupný. Zobrazuje se verze "en".Abstrakt

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.