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sav08:dpll_algorithm_for_sat [2008/03/12 18:25] vkuncak |
sav08:dpll_algorithm_for_sat [2008/03/12 19:31] vkuncak |
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Then combine these two trees with resolution on $\{p\}$ and $\{\lnot p\}$ to get ${\it false}$. | Then combine these two trees with resolution on $\{p\}$ and $\{\lnot p\}$ to get ${\it false}$. | ||
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+ | Why can we modify resolution proof to move $p$ from assumption and put its negation to conclusion? | ||
++++ | ++++ | ||
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+ | === Lower Bounds on Running Time === | ||
Observation: constructed resolution proof is polynomial in the running time of the DPLL algorithm. | Observation: constructed resolution proof is polynomial in the running time of the DPLL algorithm. | ||
- | Theorem: for some formulas, the 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 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: | ||
+ | * Pavel Pudlák: [[http://citeseer.ist.psu.edu/36219.html|Lower Bounds for Resolution and Cutting Plane Proofs and Monotone Computations]] | ||
- | ===== DPLL Imperatively ===== | ||
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- | Selecting order of variables. | ||
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- | Lemma learning. |