Optimal satisfiability for propositional calculi and constraint satisfaction problems

We consider the problems of finding the lexicographically minimal (or maximal) satisfying assignment of propositional formulas for different restricted classes of formulas. It turns out that for each class from our framework, these problems are either polynomial time solvable or complete for OptP. We also consider the problem of deciding if in the optimal assignment the largest variable gets value 1. We show that this problem is either in P or PNP complete.

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