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What is the complexity for converting any propositional formula to CNF format? Is it an NP-complete problem?
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A compound proposition is in Conjunctive Normal Form (CNF) if it is a conjunction of disjunctions. In other words, a CNF is an AND of ORs. (p ∨ ¬q) ∧ (¬ p ∨ q) ∧ (p ∨ q)
What Does Conjunctive Normal Form (CNF) Mean? Conjunctive normal form (CNF) is an approach to Boolean logic that expresses formulas as conjunctions of clauses with an AND or OR. Each clause connected by a conjunction, or AND, must be either a literal or contain a disjunction, or OR operator.
The standard algorithm to transform a general Well-Formed Formula to an equivalent CNF has an exponential run time, since in the worst case a n-clauses WFF is equivalento to a 2^n-clauses CNF.
However, you can transform in polynomial time an arbitrary boolean formula into a CNF that is not stricty equivalent, but satisfable only if the boolean formula is satisfable. This is the standard reduction used to prove that 3CNF is NP-complete, givent that the more general SAT is NP-complete. See here.
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