COMS W3261
Computer Science Theory
Lecture 17: November 19, 2012
The Classes P and NP

Outline

1. Review

2. Polynomial-Time Reductions and NP-Complete Problems

3. Boolean Expressions

4. The Satisfiability Problem

5. Normal Forms for Boolean Expressions

6. The Problems CSAT and kSAT

7. SAT is NP-complete: the Cook-Levin theorem

8. Practice Problems

  1. Is f(n) = nlog2 n (a) exponential, (b) polynomial?
  2. List all satisfying truth assignments for x ∧ (y ∧ x) ∧ (z ∨ y).
  3. Show that if A is NP-complete and A is in P, then P = NP.
  4. Show that if A is NP-complete and A is polynomially reducible to a problem B in NP, then B is NP-complete.

9. Reading Assignment



aho@cs.columbia.edu