lecture3 - CSci 5403 COMPLEXITY THEORY are just like...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 COMPLEXITY THEORY CSci 5403 LECTURE III: NOW WITH 66% MORE NP-COMPLETENESS!! NON-DETERMINISTIC PROGRAMS …are just like standard programs, except: 1. There is a special instruction, guess(), that can return 0 or 1. 2. The program accepts an input if there exists a set of guesses that make it accept. 3. The running time of the program is the maximum number of steps that can be caused by calls to guess(). NP = NTIME(n c ) c N { L | L is decided by a O(t(n))-time non-deterministic Turing machine } Definition: NTIME(t(n)) = A language is in NP if and only if there exist polynomial-length certificates for membership to the language Definition: A language B is NP-complete if: 1. B NP 2. Every A in NP is poly-time reducible to B (i.e. B is NP-hard) HARDEST PROBLEMS IN NP Theorem. C DTM is NP-Complete. Let C DTM = { ʪ M,x,t , ʫ | 9 y ˥ {0,1} . M(x,y) accepts in · t steps}
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Theorem (Cook-Levin): 3SAT is NP-complete Proof: (1) 3SAT NP (2) Every language A in NP is polynomial time reducible to 3SAT Our proof of (2) will have two steps. (a) C
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/21/2011 for the course CSCI 5403 taught by Professor Sturtivant,c during the Spring '08 term at Minnesota.

Page1 / 6

lecture3 - CSci 5403 COMPLEXITY THEORY are just like...

This preview shows document pages 1 - 3. Sign up to view the full document.

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