On Improving the Backjump Level in PB Solvers

TL;DR

This paper investigates the limitations of the 1-UIP property in PB solvers, demonstrating that it does not guarantee optimal backjumps, and proposes methods to improve backjump levels during conflict analysis.

Contribution

It reveals the non-guarantee of optimal backjumps in PB solvers due to 1-UIP limitations and introduces approaches to enhance backjump levels.

Findings

Sub-optimal backjumps are common in PB solvers.

Improved conflict analysis methods can enhance backjump levels.

Impact of sub-optimal backjumps on solver performance remains unclear.

Abstract

Current PB solvers implement many techniques inspired by the CDCL architecture of modern SAT solvers, so as to benefit from its practical efficiency. However, they also need to deal with the fact that many of the properties leveraged by this architecture are no longer true when considering PB constraints. In this paper, we focus on one of these properties, namely the optimality of the so-called first unique implication point (1-UIP). While it is well known that learning the first assertive clause produced during conflict analysis ensures to perform the highest possible backjump in a SAT solver, we show that there is no such guarantee in the presence of PB constraints. We also introduce and evaluate different approaches designed to improve the backjump level identified during conflict analysis by allowing to continue the analysis after reaching the 1-UIP. Our experiments show that sub-optimal backjumps are fairly common in PB solvers, even though their impact on the solver is not clear.