On the expressive power of unit resolution
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This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we propose to call propagatable functions, is given. By establishing that propagatable functions can also be computed using monotone circuits, we show that there exist polynomial time complexity propagable functions requiring an exponential amount of clauses to be computed using unit resolution. These results shed new light on studying CNF encodings of NP-complete problems in order to solve them using propositional satisfiability algorithms.
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