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Description
  • 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.
  • 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. (en)
Title
  • A note on SAT algorithms and proof complexity
  • A note on SAT algorithms and proof complexity (en)
skos:prefLabel
  • A note on SAT algorithms and proof complexity
  • A note on SAT algorithms and proof complexity (en)
skos:notation
  • RIV/00216208:11320/12:10126432!RIV13-MSM-11320___
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  • complexity; Computational (en)
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  • 112
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  • Krajíček, Jan
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  • 000303959300007
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  • 0020-0190
number of pages
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  • 10.1016/j.ipl.2012.03.009
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  • 11320
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