Languages Represented by Boolean Formulas

A propositional problem is a problem whose instances are defined by Boolean formulas. Using quantifier free logical reductions, we give a sufficient condition under which a large class of propositional problems becomes exponentially harder than their ordinary encodings. This result extends former upgrading results which hold only for representation by Boolean circuits. It follows that all succinct circuit problems proved complete by Papadimitriou (1994) remain complete under representation by Boolean formulas.

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