TITLE: Converting each formula into Conjunctive Normal Form?
QUESTION [6 upvotes]: How hard is it to translate an arbitrary well-formed formula into CNF formula? It seems it can get exponential in some occasions like $(a\wedge b)\vee (c\wedge d)$ is transformed into $(a\vee c)\wedge(a\vee d)\wedge (b\vee d)\wedge (b\vee c)$, in which the size of the formula seems to expand exponentially. Therefore, I feel the problem should be in NPC. However, I do not have a clue of how to reduce this problem.

REPLY [4 votes]: There are various ways to convert formulas to CNF avoiding the exponential growth of your example.
Wikipedia's Conversion_into_CNF shows how to do that. A good reference is the Handbook of Satisfiability, Chapter 2, CNF Encodings.