Binary Decision Diagrams for Affine Approximation

TL;DR

This paper introduces a new algorithm using reduced ordered binary decision diagrams (ROBDDs) for affine approximation of propositional knowledge bases, offering a more compact and efficient alternative to existing methods.

Contribution

It proposes a novel ROBDD-based algorithm for affine approximation, improving compactness and efficiency over previous set-of-models and modulo 2 congruence approaches.

Findings

ROBDD-based representation is more compact than sets of models.

The new algorithm is more efficient for affine approximation tasks.

Affine functions can be effectively approximated using the proposed method.

Abstract

Selman and Kautz's work on ``knowledge compilation'' established how approximation (strengthening and/or weakening) of a propositional knowledge-base can be used to speed up query processing, at the expense of completeness. In this classical approach, querying uses Horn over- and under-approximations of a given knowledge-base, which is represented as a propositional formula in conjunctive normal form (CNF). Along with the class of Horn functions, one could imagine other Boolean function classes that might serve the same purpose, owing to attractive deduction-computational properties similar to those of the Horn functions. Indeed, Zanuttini has suggested that the class of affine Boolean functions could be useful in knowledge compilation and has presented an affine approximation algorithm. Since CNF is awkward for presenting affine functions, Zanuttini considers both a sets-of-models representation and the use of modulo 2 congruence equations. In this paper, we propose an algorithm based on reduced ordered binary decision diagrams (ROBDDs). This leads to a representation which is more compact than the sets of models and, once we have established some useful properties of affine Boolean functions, a more efficient algorithm.