BIG Backbones

The backbone of a satisfiable formula is the set of literals that hold true in every model. In this paper we introduce Single Unit Resolution Backbone (SURB) which names both a polynomial-time algorithm for backbone extraction and a class of propositional formulas on which it is complete. We show that this class is a superset of the polynomial-time solvable SLUR formulas. The presented algorithm meets a lower bound on time complexity under the strong exponential-time hypothesis. As a second contribution, we present a version that operates on the binary implication graph (BIG) and implement it as a preprocessor in the recently introduced backbone extractor CADIBACK. Experiments on a large number of SAT competition benchmarks show that our implementation results in faster BIG backbone extraction by an order of magnitude. Additionally, incorporating it as a preprocessor enables CADIBACK to identify up to four times as many backbone literals early on.