We consider the problems of finding the lexicographically minimal (or
maximal) satisfying assignment of propositional formulae for different
restricted formula classes. It turns out that for each class from our
framework, the above problem is 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 P^NP
complete.Comment: 17 pages, 1 figur