On selecting a satisfying truth assignment

The complexity of certain natural generalizations of satisfiability, in which one of the possibly exponentially many satisfying truth assignments must be selected, is studied. Two natural selection criteria, default preference and minimality (circumscription), are considered. The thrust of the complexity results seems to be that hard problems become harder, while easy problems remain easy. This consideration yields as a byproduct a new and very natural polynomial-time randomized algorithm for 2SAT.<
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