Editing Boolean satisfiability problem (section)

===Disjunctive normal form===
SAT is trivial if the formulas are restricted to those in '''[[disjunctive normal form]]''', that is, they are a disjunction of conjunctions of literals. Such a formula is indeed satisfiable if and only if at least one of its conjunctions is satisfiable, and a conjunction is satisfiable if and only if it does not contain both ''x'' and NOT ''x'' for some variable ''x''. This can be checked in linear time. Furthermore, if they are restricted to being in '''full disjunctive normal form''', in which every variable appears exactly once in every conjunction, they can be checked in constant time (each conjunction represents one satisfying assignment).  But it can take exponential time and space to convert a general SAT problem to disjunctive normal form; to obtain an example, exchange "∧" and "∨" in the [[#Definitions|above]] exponential blow-up example for conjunctive normal forms.