## A Sharp Threshold in Proof Complexity Yields Lower Bounds for Satisfiability Search

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Citations: | 11 - 3 self |

### BibTeX

@MISC{Achlioptas_asharp,

author = {Dimitris Achlioptas and Paul Beame and Michael Molloy},

title = {A Sharp Threshold in Proof Complexity Yields Lower Bounds for Satisfiability Search},

year = {}

}

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### Abstract

We give the first example of a sharp threshold in proof complexity. More precisely, we show that for any sufficiently small > 0 and > 2:28, random formulas consisting of (1 )n 2-clauses and n 3-clauses, which are known to be unsatisfiable almost certainly, almost certainly require resolution and Davis-Putnam proofs of unsatisfiability of exponential size, whereas it is easily seen that random formulas with (1 + )n 2-clauses (and n 3-clauses) have linear size proofs of unsatisfiability almost certainly. A consequence of our result also yields the first proof that typical random 3-CNF formulas at ratios below the generally accepted range of the satisfiability threshold (and thus expected to be satisfiable almost certainly) cause natural Davis-Putnam algorithms to take exponential time to find satisfying assignments. 1