14. P and NP, SAT, Poly-Time Reducibility

MIT 18.404J Theory of Computation, Fall 2020
Instructor: Michael Sipser

NOTE: There is no video for Lecture 13 as that was the day for the Midterm Exam.

Quickly reviewed last lecture. Defined NTIME(t(n)) complexity classes and the class NP. Showed that COMPOSITES is in NP. Discussed the P versus NP question. Proved that acceptance problem for CFG is in P. Introduced the satisfiability problem SAT and polynomial-time reducibility.

License: Creative Commons BY-NC-SA

[mitocw]

*There is no video for Lecture 13 as that was the day for the Midterm Exam.*

[tanmaysingal]

Don't understand why (a) is not a solution for check-in 14.1.

Consider the NTM which decides whether <G, s, t> \in HAMPATH or not.

NTM *decides* this in poly(m) time, where m = size of input (say, the number of vertices).

Thus, NTM is able to accept or reject input in poly (m).

Since it is also able to reject in poly(m) time, why can't you invert the solution?

Or am I wrong in believing that it can also reject in poly(m) time?

[thhiep]

What is the difference between "testing" and "verifying"?

[QT-ytdb]

It is a very good series of videos, but it has a caveat. Professor Sipster seems to try to explain in detail without first giving a definite answer....

[MichaelSt]

Why do we say that for a NTM decider, all branches halt on all inputs?
By "branches halt" do we include the possibility of one of the branches having an accepting state and hence all the other branches halt when we find that accepting state? (Since if the NTM finds an accepting state it halts).

[djhi-tek]

Why aren't there black cs professors?