Lecture16 - 15-453 FORMAL LANGUAGES AUTOMATA AND...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
FORMAL LANGUAGES, AUTOMATA AND COMPUTABILITY 15-453
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
NP = NTIME(n k ) k N
Background image of page 2
Theorem: L NP if there exists a poly-time Turing machine V( erifier ) with L = { x | 5 y ( witness ) |y| = poly(|x|) and V(x,y) accepts } Proof: (1) If L = { x | 5 y |y| = poly(|x|) and V(x,y) accepts } then L NP Because we can guess y and then run V (2) If L NP then L = { x | 5 y |y| = poly(|x|) and V(x,y) accepts } Let N be a non-deterministic poly-time TM that decides L and define V(x,y) to accept if y is an accepting computation history of N on x
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
A language is in NP if and only if there exist polynomial-length certificates for membership to the language SAT is in NP because a satisfying assignment is a polynomial-length certificate that a formula is satisfiable
Background image of page 4
NP = all the problems for which once you have the answer it is easy (i.e. efficient) to verify
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
P = NP?
Background image of page 6
If P = NP… Cryptography as we know it would not be possible (e.g. RSA) Mathematicians would be out of a job AI program become perfect as exhaustive search is efficient
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
If P = NP… Writing symphonies is as easy as listening to them. Being a chef is as easy as eating. Writing Shakespeare is as easy as recognizing Shakespeare. Generation is as easy as recognition :
Background image of page 8
POLY-TIME REDUCIBILITY A language A is polynomial time reducible to language B, written A P B , if there is a polynomial time computable function f : Σ* Σ*, where for every w, w A f(w) B f is called a polynomial time reduction of A to B
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/29/2012 for the course CS 15-453 taught by Professor Edmundm.clarke during the Spring '09 term at Carnegie Mellon.

Page1 / 38

Lecture16 - 15-453 FORMAL LANGUAGES AUTOMATA AND...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online