Satisfiability Checking - Fourier–Motzkin Variable Elimination
Satisfiability Checking - Fourier–Motzkin Variable Elimination
Satisfiability Checking - Fourier–Motzkin Variable Elimination
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Partitioning the Constraints<br />
1. When eliminating xn, partition the constraints according to the<br />
coefficient ain:<br />
ain > 0: upper bound βi<br />
ain < 0: lower bound βi<br />
n<br />
aij · xj ≤ bi<br />
j=1<br />
n−1<br />
⇒ ain · xn ≤ bi −<br />
⇒ xn ≤ bi<br />
ain<br />
−<br />
aij · xj<br />
j=1<br />
n−1<br />
aij<br />
ain<br />
j=1<br />
· xj =: βi<br />
Prof. Dr. Erika Ábrahám - <strong>Satisfiability</strong> <strong>Checking</strong> 6 / 10
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