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Optimization and probabilistic satisfiability on nested and co-nested formulas

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Abstract

Nested and co-nested formulas are two classes of CNF instances that can be characterized in terms of outerplanar graphs. For these classes, linear time algorithms are known for SAT and (unweighted) Max-SAT. In this paper we devise linear time algorithms for a general optimization version of SAT. Moreover, we show that a general probabilistic version of SAT reduces to solving a system of linear inequalities where the number of variables and constraints is linear in the size of the formula.

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Correspondence to Daniele Pretolani.

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Pretolani, D. Optimization and probabilistic satisfiability on nested and co-nested formulas. Ann Oper Res 188, 371–387 (2011). https://doi.org/10.1007/s10479-008-0502-3

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