A Verified Decision Procedure for Pseudo-Boolean Formulas

Pseudo-Boolean formulas consist of constraints of the form ∑i=1 wi · xi k, where xi are propositional literals, wi ∈ Z, k ∈ Z, and arise in planning, scheduling and optimization problems. We describe an efficient and easily verifiable decision procedure for pseudo-Boolean formulas, that is based on encoding PB formulas into the propositional satisfiability problem with the cutting-edge sequential weighted counter encoding. State-of-the-art SAT solvers that emit unsatisfiability proofs are used to solve the resulting instances. The combination of a verified translation to SAT, and certified SAT solvers leads to a verified decision procedure for PB formulas. The verification of the encoding is carried out in the Coq proof assistant.

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