Simplifying Pseudo-Boolean Constraints in Residual Number Systems

ABSTRACT. We present an encoding of pseudo-Boolean constraints based on decomposition with respect to a residual number system. We illustrate that careful selection of the base for the residual number system, and when bit-blasting modulo arithmetic, results in a powerful approach when solving hard pseudo-Boolean constraints. We demonstrate, using a range of pseudo-Boolean constraint solvers, that the obtained constraints are often substantially easier to solve.