Ordered binary decision diagrams and the Shannon effect

Ordered binary decision diagrams and the Shannon effect

We investigate the size and structure of ordered binary decision diagrams (OBDDs) for random Boolean functions. It was known that for most values of n, the expected OBDD size of a random Boolean function with n variables is equal to the worst-case size up to terms of lower order. Such a phenomenon is generally called strong Shannon effect. Here we show that the strong Shannon effect is not vali...

Learning Ordered Binary Decision Diagrams

This note studies the learnability of ordered binary decision diagrams (obdds). We give a polynomial-time algorithm using membership and equivalence queries that nds 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 ...

Ordered Binary Decision Diagrams and Minimal Trellises

Ordered binary decision diagrams (OBDDs) are graph-based data structures for representing Boolean functions. They have found widespread use in computer-aided design and in formal veriication of digital circuits. Minimal trellises are graphical representations of error-correcting codes that play a prominent role in coding theory. This paper establishes a close connection between these two graphi...

Ordered Binary Decision Diagrams as Knowledge-Bases

Composition of Reduced Ordered Binary Decision Diagrams

A widely accepted opinion is that, under a certain ordering restriction, the class of Reduced Ordered Binary Decision Diagrams (ROBDDs) is closed under composition. However, in this paper we show that this is not correct. We formulate necessary and sufficient conditions for the composition of two ROBDDs to result in a non-reduced OBDD. Ignoring these conditions may lead to an incorrect conclusi...