next up previous
Next: Up: Previous:

CNF Satisfiability

When the full power of SAT is not required to prove a language is in NPC, 3-CNF provides a more constrained alternative.

k-CNF (Conjunctive Normal Form) is a formula having a conjunction of clauses, where each clause is a disjunction of exactly k literals (variable or its negation).

Example 3-CNF: \((x_1 \;\vee\; x_2 \;\vee\; x_3) \;\wedge\;
(x_4 \;\vee\; \neg x_2 \;\vee\; x_4)\)

Theorem 34.10

3-CNF-SAT $\in$ NPC


next up previous
Next: Up: Previous: