Let's see this example: Max weighted sat. We have a collection of clauses. Every clause i has associated a weight. Clause C(i) has an associated weight w(i). And every clause is the disjunction of a set of k(i) literals. The literals are selected out of n different Boolean variables. So, this means that every literal is either a negated or an unnegated Boolean variable. So the goal in the max weighted sat problem is to find an assignment of the variables in a way that we maximize the weight of satisfied clauses.

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