hwsol1.4 - Example solution: 1.4 Avery Musbach February 9,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Page1 / 2

hwsol1.4 - Example solution: 1.4 Avery Musbach February 9,...

This preview shows document pages 1 - 2. Sign up to view the full document.

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