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sav07_lecture_3_skeleton [2007/03/21 10:17] vkuncak |
sav07_lecture_3_skeleton [2007/03/21 10:39] vkuncak |
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Proof: small model theorem. | Proof: small model theorem. | ||
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Next: reduce to integer linear programming: | Next: reduce to integer linear programming: | ||
\begin{equation*} | \begin{equation*} | ||
- | Ax = b, x \geq 0 | + | A\vec x = \vec b, \qquad \vec x \geq \vec 0 |
\end{equation*} | \end{equation*} | ||
where $A \in {\cal Z}^{m,n}$ and $x \in {\cal Z}^n$. | where $A \in {\cal Z}^{m,n}$ and $x \in {\cal Z}^n$. | ||
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Moreover, one can improve these bounds. One tool based on these ideas is [[http://www.cs.cmu.edu/~uclid/|UCLID]]. | Moreover, one can improve these bounds. One tool based on these ideas is [[http://www.cs.cmu.edu/~uclid/|UCLID]]. | ||
- | Alternative: enumerate disjuncts of DNF on demand, each disjunct is a conjunction, then use ILP techniques (often first solve the underlying linear programming problem over reals). Most SMT tools are based on this idea (along with Nelson-Oppen combination: next class). | + | Alternative: enumerate disjuncts of DNF on demand, each disjunct is a conjunction, then use ILP techniques (often first solve the underlying linear programming problem over reals). Many SMT tools are based on this idea (along with Nelson-Oppen combination: next class). |
* [[http://www.cs.nyu.edu/acsys/cvc3/download.html|CVC3]] (successor of CVC Lite) | * [[http://www.cs.nyu.edu/acsys/cvc3/download.html|CVC3]] (successor of CVC Lite) | ||
* [[http://combination.cs.uiowa.edu/smtlib/|SMT-LIB]] Standard for formulas, competition | * [[http://combination.cs.uiowa.edu/smtlib/|SMT-LIB]] Standard for formulas, competition |