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| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
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sav07_lecture_3_skeleton [2007/03/21 11:01] vkuncak |
sav07_lecture_3_skeleton [2007/03/21 11:04] vkuncak |
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| R( c ) -> error=false | R( c ) -> error=false | ||
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| R(havoc x) = frame(x) | R(havoc x) = frame(x) | ||
| - | R(assume F) = F[x:=x_0, y:=y_0, error:=error_0] | + | R(assume F) = F[x:=x_0, y:=y_0, error:=error_0] & frame() |
| R(assert F) = (F -> frame) | R(assert F) = (F -> frame) | ||
| Line 185: | Line 186: | ||
| Proof: small model theorem. | Proof: small model theorem. | ||
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| Line 213: | Line 215: | ||
| * solution of Ax=b (A regular) has as components rationals of form p/q with bounded p,q | * solution of Ax=b (A regular) has as components rationals of form p/q with bounded p,q | ||
| * duality of linear programming | * duality of linear programming | ||
| - | * obtains bound $M = n(ma)^{2m+1}$, which needs $(2m+1)(\log n + \log m + \log a)$ bits | + | * obtains bound $M = n(ma)^{2m+1}$, which needs $\log n + (2m+1)\log(ma)$ bits |
| * we could encode the problem into SAT: use circuits for addition, comparison etc. | * we could encode the problem into SAT: use circuits for addition, comparison etc. | ||