Boolean Satisfiability (SAT) Algorithms

Interpolants from Proofs
A = (p)(¬p∨q) B = (¬q∨r) (¬ r)
(p) (¬p∨q)
(q)
(¬q∨r) (¬r)
(p) is root and ∈ A
but global literals = ∅
False
(¬p∨q) is root and ∈ A
global literals = {q}
(q)
(r)
()
itp(c) { // c ∈ VΠ let p(c) be a
if c is a root, then
if c ∈ A then
itp(c) = the disjunction of the global literals in c
else itp(c) = constant True
else, let c1, c2 be the predecessors of c
and let v be their pivot variable
if v is local to A
then itp(c) = itp(c1) ∨ itp(c2)
else p(c) = p(c1) ∧ p(c2)
}
(q) is not root
p is local to A
(r) is not root
q is not local
True
True (¬r) is root,
but ∉A
q A’
(¬q∨r) is root,
but ∉A
() is not root
r is not local
Boolean SAT Algorithms / FLOLAC 2009 Prof. Chung-Yang (Ric) Huang http://dvlab.ee.ntu.edu.tw
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