## A sharp threshold in proof complexity (2001)

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Venue: | PROCEEDINGS OF STOC 2001 |

Citations: | 52 - 13 self |

### BibTeX

@INPROCEEDINGS{Achlioptas01asharp,

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

title = {A sharp threshold in proof complexity},

booktitle = {PROCEEDINGS OF STOC 2001 },

year = {2001},

pages = {337--346},

publisher = {}

}

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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 � and � � �, random formulas consisting of 2-clauses and 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 2-clauses (and 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.