This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Example solution: 1.4 Avery Musbach February 9, 2010 (a) We claim that a language L ⊆ { , 1 } * is in roNTIME ( f ( n )) iff there exists a polynomial p : N → N , a natural number c ∈ N and a f ( n c )time TM M (which I shall call the verifier for L ) such that for every x ∈ { , 1 } * , x ∈ L ⇐⇒ ∃ u ∈{ , 1 } f ( p (  x  )) M ( x,u ). If x ∈ L and u ∈ { , 1 } f ( p (  x  )) satisfy M ( x,u ), then we shall call u a certificate for x (with respect to the language L and machine M ). Suppose L is decided by a NDTM N that runs in time f ( n c ) (for some c ∈ N ). For every x ∈ L , there is a sequence of nondeterministic choices that makes N reach q accept on input x . We can use this sequence as a certificate for x . This certificate has length f (  x  c ) and can be verified in O ( f ( n c )) time by a deterministic Turing machine, which simulates the action of N using these nondeterministic choices....
View
Full
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.
 Spring '08
 Sturtivant,C

Click to edit the document details