Abstract

This note studies the learnability of ordered binary decision diagrams (obdds). We give a polynomial-time algorithm using membership and equivalence queries that finds the minimum obdd for the target respecting a given ordering. We also prove that both types of queries and the restriction to a given ordering are necessary if we want minimality in the output, unless P=NP. If learning has to occur with respect to the optimal variable ordering, polynomial-time learnability implies the approximability of two NP-hard optimization problems: the problem of finding the optimal variable ordering for a given obdd and the Optimal Linear Arrangement problem on graphs. 1 Introduction The representation of boolean functions as ordered binary decision diagrams (obdds) has received great attention recently. This representation has nice computational properties for fixed variable ordering such as the existence of a minimum canonical form and, efficient algorithms for elementary boolean operations, sat...

Citations