Optimizing backbone filtering

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• We propose a tool in TASE'17 named DUCIBone. • We propose an extension of DUCIBone named EDUCIBone. • COV, WHIT, and 2LEN are newly introduced in EDUCIBone. • New benchmarks are included. • EDUCIBone still outperforms minibones-cb100, and DUCIBone. In propositional formulas, literals are assigned to True or False in each assignment. Backbone literals are always assigned to True in every satisfiable assignment (model) of the given formula. Backbone literals are keys to improve the performance of SAT testing and SAT-based applications, such as model checking and program analysis. In this paper, we propose an optimized approach that combines COV, WHIT and 2LEN strategies to improve backbone computing. We have implemented it in EDUCIBone . COV and 2LEN are used for finding backbone literals, WHIT is used for finding non-backbone literals. COV uses the fact that for a backbone literal l , there must exist at least one clause ϕ in every model v of the given formula Φ such that for every other literal l ′ in ϕ , the assignment of l ′ is False in v . WHIT is based on the fact that for a literal l , and a model v of the given formula Φ, if for every clause ϕ that has l , there always exists another l ′ also in ϕ such that the assignment of l ′ is True, then l is a non-backbone literal. For a literal l , the naive way to decide if l is a backbone literal is to check the satisfiability of l ∧ Φ and ¬ l ∧ Φ . 2LEN finds a set of unique free literals F l for l , such that the satisfiability of ¬ l ∧ Φ and ⋀ l ′ ∈ F l l ′ ∧ Φ are the same. Experiments show that checking the satisfiability of ⋀ l ′ ∈ F l l ′ ∧ Φ is faster than checking the satisfiability of ¬ l ∧ Φ when the backbone computing time of the given formula is less than 3000 seconds. We deactivate 2LEN strategy when the formula has been computed for more than 3000 seconds. We evaluate the performance of EDUCIBone on formulas from industrial tracks in SAT Competitions from 2011 to 2017. Performance comparisons are conducted among EDUCIBone , DUCIBone and minibones-cb100 . Results show that EDUCIBone solves the most formulas. For the formulas that are commonly solved by the three tools, EDUCIBone is the fastest in computing backbone literals from the formulas. We also analyze the efficiency of COV, WHIT and 2LEN strategies separately with detailed experiments. Results show that every strategy contributes to the performance of EDUCIBone , and they are all applied to various kinds of formulas.