Optimizing backbone filtering

Backbone is the common part of each solution in a given propositional formula, which is a key to improving the performance of SAT solving and SAT-based applications, such as model checking and program analysis. In this paper, we propose an optimized approach that combines implication-driven (IDF), conflict-driven (CDF), and unique-driven (UDF) heuristics to improve backbone computing. IDF uses the particular binary structure of the form a ↔ b ∧ c to find more backbone literals. CDF comes from the observation that for a clause ¬a ∨ b, if a is a backbone literal, then b is also a backbone literal. Besides CDF, we are also able to detect new non-backbone literals by UDF. A literal l is not a backbone literal, if there is no clause φ ∈ Φ that is only satisfied by l. We implemented our approach in a tool named DUCIBone with the above optimizations (IDF+CDF+UDF), and conducted experiments on formulas used in previous work and SAT competitions (2015, 2016). Results demonstrate that DUCIBone solved 4% (507 formulas) more formulas than minibones (minibones-RLD, 490 formulas) does under its best configuration. Among 486 formulas solved by all tools (DUCIBone, minibones-RLD, minibonescb100), DUCIBone reduced 7% (35131 seconds) than minibones (37454 seconds). Experiments indicate that the advantage of DUCIBone is more obvious when the formulas are harder.