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sav08:dpll_algorithm_for_sat [2008/03/13 17:46] vkuncak |
sav08:dpll_algorithm_for_sat [2013/04/17 17:35] vkuncak |
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S' \vdash {\it false} | S' \vdash {\it false} | ||
\] | \] | ||
- | ++++Idea:| | ||
From | From | ||
\[ | \[ | ||
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Why can we modify resolution proof to move $p$ from assumption and put its negation to conclusion? | Why can we modify resolution proof to move $p$ from assumption and put its negation to conclusion? | ||
- | ++++ | + | |
=== Lower Bounds on Running Time === | === Lower Bounds on Running Time === | ||
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Theorem: for some formulas, shortest resolution proofs are exponential. | Theorem: for some formulas, shortest resolution proofs are exponential. | ||
- | This does not contradict P vs NP question, because there may be "better" proof systems than resolution. | + | This does not contradict that P vs NP question is open, 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 (see [[Interpolants from Resolution Proofs]]): | 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]] |