This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ean that these problems are also NPcomplete; they are in NP and also as hard as any problem in NP . If their solvability in deterministic polynomial time were resolved, the P versus NP question would be solved. The question of whether P = NP is the central unsolved question of computational complexity theory, and no one expects it to be solved anytime soon. If someone showed that P = NP, then most of this book would be irrelevant: As previously explained, many classes of ciphers are trivially breakable in nondeterministic polynomial time. If P = NP, they are breakable by feasible, deterministic algorithms. Further out in the complexity hierarchy is PSPACE . Problems in PSPACE can be solved in polynomial space, but not necessarily polynomial time. PSPACE includes NP, but some problems in PSPACE are thought to be harder than NP. Of course, this isn’t proven either. There is a class of problems, the socalled PSPACEcomplete problems, with the property that, if any one of them is in NP then PSPACE = NP and if any one of them is in P then PSPACE = P . And finally, there is the class of problems called EXPTIME . These problems are solvable in exponential time. The EXPTIMEcomplete problems can actually be proven not to be solvable in deterministic polynomial time. It has been shown that P does not equal EXPTIME . Previous Table of Contents Next Products  Contact Us  About Us  Privacy  Ad Info  Home Use of this site is subject to certain Terms & Conditions, Copyright © 19962000 EarthWeb Inc. All rights reserved. Reproduction whole or in part in any form or medium without express written permission of EarthWeb is prohibited. Read EarthWeb's privacy statement. To access the contents, click the chapter and section titles. Applied Cryptography, Second Edition: Protocols, Algorthms, and Source Code in C (cloth)
Go!
Keyword
Brief Full Advanced Search Search Tips (Publisher: John Wiley & Sons, Inc.) Author(s): Bruce Schneier ISBN: 0471128457 Publication Date: 01/01/96 Search this book:
Go! Previous Table of Contents Next
 NPComplete Problems
Michael Garey and David Johnson compiled a list of over 300 NPcomplete problems [600]. Here are just a few of them: — Traveling Salesman Problem. A traveling salesman has to visit n different cities using only one tank of gas (there is a maximum distance he can travel). Is there a route that allows him to visit each city exactly once on that single tank of gas? (This is a generalization of the Ha...
View
Full
Document
This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
 Fall '10
 ALIULGER
 Cryptography

Click to edit the document details