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sav07_lecture_3_skeleton [2007/03/21 10:01] vkuncak |
sav07_lecture_3_skeleton [2007/03/21 10:15] vkuncak |
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| Proof: small model theorem. | Proof: small model theorem. | ||
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| We can prove small model theorem for ILP - gives bound on search. | We can prove small model theorem for ILP - gives bound on search. | ||
| - | Short proof by {{papadimitriou81complexityintegerprogramming.pdf|Papadimitriou}}. | + | Short proof by {{papadimitriou81complexityintegerprogramming.pdf|Papadimitriou}}: |
| + | * solution of Ax=b (A regular) has as components rationals of form p/q with bounded p,q | ||
| + | * duality of linear programming | ||
| + | * obtains bound $M = n(ma)^{2m+1}$. | ||
| Note: if small model theorem applies to conjunctions, it also applies to arbitrary QFPA formulas. Moreover, one can improve these bounds. One tool based on these ideas is [[http://www.cs.cmu.edu/~uclid/|UCLID]]. | Note: if small model theorem applies to conjunctions, it also applies to arbitrary QFPA formulas. Moreover, one can improve these bounds. One tool based on these ideas is [[http://www.cs.cmu.edu/~uclid/|UCLID]]. | ||