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Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
sav08:dpll_algorithm_for_sat [2008/03/12 19:31] vkuncak |
sav08:dpll_algorithm_for_sat [2008/03/13 17:45] vkuncak |
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<code> | <code> | ||
def DPLL(S : Set[Clause]) : boolean = | def DPLL(S : Set[Clause]) : boolean = | ||
- | val S' = BCP(S) | + | val S' = RemoveSubsumed(BCP(S)) |
if (emptyClause in S') then false | if (emptyClause in S') then false | ||
else if (S' has only unit clauses) then true | else if (S' has only unit clauses) then true | ||
Line 39: | Line 39: | ||
val P = pick variable from FV(S') | val P = pick variable from FV(S') | ||
DPLL(F' union {p}) or DPLL(F' union {Not(p)}) | DPLL(F' union {p}) or DPLL(F' union {Not(p)}) | ||
+ | </code> | ||
+ | |||
+ | <code> | ||
+ | def RemoveSubsumed(S : Set[Clause]) : Set[Clause] = | ||
+ | if there are C1,C2 in S such that C1 subset C2 | ||
+ | then RemoveSubsumes(S - {C2}) | ||
+ | else S | ||
</code> | </code> | ||
Line 121: | Line 128: | ||
This does not contradict P vs NP question, because there may be "better" proof systems than resolution. | This does not contradict P vs NP question, because there may be "better" proof systems than resolution. | ||
- | Lower bounds for both resolution and a stronger system are shown here by proving that interpolants can be exponential, and that interpolants are polynomial in proof size: | + | Lower bounds for both resolution and a stronger system are shown here by proving that interpolants can be exponential, and that interpolants are polynomial in proof size (see [[Interpolants from Resolution Proofs]]): |
* Pavel Pudlák: [[http://citeseer.ist.psu.edu/36219.html|Lower Bounds for Resolution and Cutting Plane Proofs and Monotone Computations]] | * Pavel Pudlák: [[http://citeseer.ist.psu.edu/36219.html|Lower Bounds for Resolution and Cutting Plane Proofs and Monotone Computations]] | ||
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