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Unformatted text preview: Handout Transformation of a formula A to a formula B in conjunctive normal form, so that A is satisifable iff B is satisfiable. Given a formula A , consider its parse tree T A . To each node a of T A associate a proposi tional variable p a , so that: i) If a is terminal, then p a = p , where p is the propositional variable occurring at a ; ii) If a is a nonterminal node, p a is different from all the propositional variables occurring in A ; iii) To distinct nodes we assign distinct variables. For each node a which is not terminal, we have one of the following five possibilities b → a → r r B ¬ B b → r B a → r ( B ∨ C ) ∨ @ @ C r ← c b → r B a → r ( B ∧ C ) ∧ @ @ C r ← c b → r B a → r ( B ⇒ C ) ⇒ @ @ C r ← c b → r B a → r ( B ⇔ C ) ⇔ @ @ C r ← c In the first case, associate to a the formula: p a ⇔ ¬ p b (1) In the second, associate to a the formula: p a ⇔ ( p b ∨ p c ) (2) In the third case, the formula: p a ⇔ ( p b ∧ p c ) (3) In the fourth case, the formula...
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This note was uploaded on 07/19/2010 for the course MA 1C taught by Professor Ramakrishnan during the Spring '08 term at Caltech.
 Spring '08
 Ramakrishnan
 Calculus, Linear Algebra, Algebra

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