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Why do satisfiability solvers require conjunctive normal form?

  • A.A single uniform rule then applies to every clause
  • B.The form is more compact than the original sentence
  • C.Only formulas in that form have models at all
  • D.The conversion removes all the negations from a sentence

Answer: A

With everything reduced to clauses, unit propagation and resolution apply uniformly and no special cases are needed for the connectives. The conversion may increase size, exponentially in the worst case unless auxiliary variables are introduced. Satisfiability is preserved rather than created, and negations remain on literals. Standardising the input so that one rule suffices, even at some cost in size, is a trade that mechanical procedures repeatedly make.

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