Publication at Faculty of Mathematics and Physics |
2012
Abstract
We apply classical proof complexity ideas to transfer lengths-of-proofs lower bounds for a propositional proof system P into examples of hard unsatisfiable formulas for a class Alg(P) of SAT algorithms determined by P. The class Alg(P) contains those algorithms M for which P proves in polynomial size tautologies expressing the soundness of M.
For example, the class Alg(F-d) determined by a depth d Frege system contains the commonly considered enhancements of DPLL (even for small d). Exponential lower bounds are known for all F-d.
Such results can be interpreted as a form of consistency of P not equal NP. Further we show how the soundness statements can be used to find hard satisfiable instances, if they exist.