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005-CNF

# Cd 6 7 a cd b cd 1 2 3 8 b cd source karem

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Unformatted text preview: chronological back-tracking – similar to circuit case 9 Conflict-based Learning 4 5 (a + b + c) 9 (a + b + ¬c) 10 (¬a + b + ¬c) 11 (a + c + d) (¬a + c + d) 6 7 (¬a + c + ¬d) (¬b + ¬c + ¬d) 1 2 3 8 (¬b + ¬c + d) Source: Karem A. Sakallah, Univ. of Michigan (¬b + ¬c) (¬a + ¬b) ab bc → ¬ϕb (¬a ) a → ¬ ϕ ⇓ ⇓c a ϕ → (¬b + ϕ → (¬a) b ¬c) a 11 a a 7 b 3 d 10 b b 7 3 c b c 99 c a b 6 6 85 45 8 c5 5d d6 6 48 d 66 10 Conflict-based Learning • Important detail for cut selection: – During implication processing, record decision level for each implication – At conflict, select earliest cut such that exactly one node of the implication graph lies on current decision level • Either decision variable itself • Or UIP (“unique implication point”) that represents a dominator node in conflict graph • By selecting such cut, implication processing will automatically flip decision variable (or UIP variable) to its complementary value 11 Further Improvements • Random restarts: – stop after a given number of backtracks • start search again with modified ordering heuristic • keep learned structures !!! – very effective for satisfiable formulas but often also effective for unsat formulas • Learning of equivalence relations: – (a ⇒ b) ∧ (b ⇒ a) ⇒ (a = b) – very powerful for formal equivalence checking 12...
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