Compiling Finite Domain Constraints to SAT with BEE: the Director's Cut

TL;DR

BEE is a compiler that translates finite domain constraints into SAT problems using equi-propagation and fragment-based reasoning, with recent enhancements including hybrid encoding and complete equi-propagation.

Contribution

This paper details undocumented implementation aspects of BEE, such as hybrid encoding and complete equi-propagation, and discusses extending BEE to binary number representations.

Findings

Enhanced encoding of cardinality constraints

Implementation of complete equi-propagation

Ongoing work on binary number representation

Abstract

BEE is a compiler which facilitates solving finite domain constraints by encoding them to CNF and applying an underlying SAT solver. In BEE constraints are modeled as Boolean functions which propagate information about equalities between Boolean literals. This information is then applied to simplify the CNF encoding of the constraints. We term this process equi-propagation. A key factor is that considering only a small fragment of a constraint model at one time enables to apply stronger, and even complete reasoning to detect equivalent literals in that fragment. Once detected, equivalences propagate to simplify the entire constraint model and facilitate further reasoning on other fragments. BEE is described in several recent papers. In this paper, after a quick review of BEE, we elaborate on two undocumented details of the implementation: the hybrid encoding of cardinality constraints and complete equi-propagation. We thendescribe on-going work aimed to extend BEE to consider binary representation of numbers.