Homework Solution: Prove Theorem 4.13 on the correctness of the CNF-to-3CNF algorithm…

    Prove Theorem 4.13 on the correctness of the CNF-to-3CNF algorithm

    Theorem 4.13 Let A be a formula in CNF and let A be the formula in 3CNF constructed from A by Algorithm 4.12. Then A is satisfiable if and only if A is satisfiable. The length of A (the number of symbols in A) is a polynomial in the length of A.

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    Theorem 4.13 Let A be a formula in CNF and let A' be the formula in 3CNF constructed from A by Algorithm 4.12. Then A is satisfiable if and only if A' is satisfiable. The length of A' (the number of symbols in A') is a polynomial in the length of A.

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    Prove Theorem 4.13 on the prevention of the CNF-to-3CNF algorithm

    Theorem 4.13 Permit A be a formula in CNF and permit A be the formula in 3CNF manufactured from A by Algorithm 4.12. Then A is satisfiable if and singly if A is satisfiable. The elongation of A (the estimate of symbols in A) is a polynomial in the elongation of A.

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    Theorem 4.13 Permit A be a formula in CNF and permit A’ be the formula in 3CNF manufactured from A by Algorithm 4.12. Then A is satisfiable if and singly if A’ is satisfiable. The elongation of A’ (the estimate of symbols in A’) is a polynomial in the elongation of A.

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