Compression with wildcards: All k-models of a binary decision diagram

TL;DR

This paper introduces a method for efficiently enumerating all models of a Boolean function with fixed Hamming-weight using compressed representations and wildcards, extending existing enumeration techniques.

Contribution

It presents a novel approach to enumerate all fixed Hamming-weight models of Boolean functions efficiently using wildcards, improving on prior enumeration methods.

Findings

Efficient enumeration of all fixed Hamming-weight models in polynomial time.

Introduction of wildcards for compressed model representation.

Extension of enumeration techniques to fixed Hamming-weight models.

Abstract

Given a Binary Decision Diagram $B$ of a Boolean function $\varphi$ in $n$ variables, it is well known that all $\varphi$-models can be enumerated in output polynomial time, and in a compressed way (using don't-care symbols). We show that all $N$ many $\varphi$-models of fixed Hamming-weight $k$ can be enumerated as well in time polynomial in $n$ and $|B|$ and $N$. Furthermore, using novel wildcards, again enables a compressed enumeration of these models.