lecture4 - P VS NP CSci 5403 Recognition vs Generation...

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

View Full Document Right Arrow Icon
COMPLEXITY THEORY CSci 5403 LECTURE IV: BEYOND P VS NP P VS NP Recognition vs Generation Checking if a song sounds like Mozart Composing a song that sounds like Mozart Checking if a proof is correct Finding a correct proof Checking if a fusion generator is efficient Finding an efficient fusion generator Verifying that p £ q = N Finding prime factors of N Appreciating funny jokes Writing funny jokes If P=NP, especially by a fast algorithm, then the tasks on left and right are all equally difficult! P vs NP is a central, motivating question for complexity theory, but also a “representative” of many related questions… NP vs coNP coNP = { L | L ̄ 2 NP } = { y | y L } Theorem. L 2 coNP iff there exists a poly-time TM V and polynomial p so that L = { x | 8 y 2 {0,1} p(y) , V(x,y) accepts } Proof. L 2 coNP means L ̄ 2 NP. Let U be the Verifier for L ̄ , and let V(x,y) = not U(x,y). x
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

lecture4 - P VS NP CSci 5403 Recognition vs Generation...

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