Many hard examples for resolution

  • Authors:
  • Vašek Chvátal;Endre Szemerédi

  • Affiliations:
  • Rutgers Univ., New Brunswick, NJ;Rutgers Univ., New Brunswick, NJ and Hungarian Academy of Sciences, Budapest, Hungary

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1988

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Abstract

For every choice of positive integers c and k such that k ≥ 3 and c2-k ≥ 0.7, there is a positive number &egr; such that, with probability tending to 1 as n tends to ∞, a randomly chosen family of cn clauses of size k over n variables is unsatisfiable, but every resolution proof of its unsatisfiability must generate at least (1 + &egr;)n clauses.