Lecture 14: CIRCUIT-SAT

October 20th, 2008

If we have an NP-Complete problem X, then we can show that a new problem Y is NP-Complete by

  • Showing that Y is in NP
  • Showing that X reduces to Y.

But where did this first NP-Complete problem come from, if there aren’t turtles all the way down…

The answer is the Cook-Levin Theorem, one of the most profound results in complexity theory:

CIRCUIT-SAT is NP-Complete

We’ll handwave a proof of this, and look at some examples to understand how the proof works.

This entry was posted on Monday, October 20th, 2008 at 12:56 pm and is filed under lectures, news.

2 Responses to “Lecture 14: CIRCUIT-SAT”

  1. Questioner Says:
    December 4th, 2008 at 8:12 pm

    Should the second line be “Showing that Y reduces to X”?
    And another question is in page 471 of the textbook, how can we get the clauses to guarantee the three different gates? Thx.

  2. admin Says:
    December 4th, 2008 at 11:57 pm

    No, the statement is correct. We have to reduce the known NPC problem X to the unknown problem Y. I’m not sure I understand the second question

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