Clause Size Reduction with all-UIP Learning

Efficient All-UIP Learned Clause Minimization

“…Minimization, in its original form [19], only removes literals from the initial deduced clause during conflict analysis, i.e., the 1st-unique-implication-point clause [22]. In 2020 Feng & Bacchus [12] revisited the all-UIP heuristics with the goal to reduce the size of the deduced clause even further by allowing to add new literals. In this paper we call such advanced minimization techniques shrinking.…”

“…In this paper we call such advanced minimization techniques shrinking. In order to avoid spending too much time in such shrinking procedures the authors of [12] had to limit its effectiveness. They also described and implemented several variants in the SAT solver CaDiCaL [2].…”

“…As Feng & Bacchus [12] consider minimization and all-UIP shrinking separately, they apply minimization first, then all-UIP shrinking, and finally again minimization (depending on the deployed strategy/variant), while we integrate both techniques into one simple algorithm. In contrast, their variants process literals of the deduced clause from highest to lowest decision level and eagerly https://doi.org/10.35011/fmvtr.2021-3 Technical Report 21/3, May 2021, FMV Reports Series Institute for Formal Models and Verification, Johannes Kepler University Altenbergerstr.…”

“…This work is based on the classical minimization algorithm [19], which Van Gelder [20] improved by making it linear (in the number of literals) in the implication graph without changing the resulting minimized clause. The original all-UIP scheme [22] was never considered to be efficient enough to be part of SAT solvers, until the work by Feng & Bacchus [12]. We refer to their work for a detailed discussion on all-UIPs.…”

“…We refer to their work for a detailed discussion on all-UIPs. Note that, Feng & Bacchus [12] consider their algorithm to be independent of minimization, more like a post-processing step, while we combine shrinking and minimization for improved efficiency. This is the extend version (with the proofs) of our SAT paper [14]…”