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Boolean MaxSAT, as well as generalized formulations such as Min-MaxSAT andMax-hybrid-SAT, are fundamental optimization problems in Boolean reasoning.Existing methods for MaxSAT have been successful in solving benchmarks in CNFformat. They lack, however, the ability to handle 1) (non-CNF) hybridconstraints, such as XORs and 2) generalized MaxSAT problems natively. Toaddress this issue, we propose a novel dynamic-programming approach for solvinggeneralized MaxSAT problems with hybrid constraints -- called\emph{Dynamic-Programming-MaxSAT} or DPMS for short -- based on AlgebraicDecision Diagrams (ADDs). With the power of ADDs and the (graded)project-join-tree builder, our versatile framework admits many generalizationsof CNF-MaxSAT, such as MaxSAT, Min-MaxSAT, and MinSAT with hybrid constraints.Moreover, DPMS scales provably well on instances with low width. Empiricalresults indicate that DPMS is able to solve certain problems quickly, whereother algorithms based on various techniques all fail. Hence, DPMS is apromising framework and opens a new line of research that invites moreinvestigation in the future.

DPMS: An ADD-Based Symbolic Approach for Generalized MaxSAT Solving