lecture13 - 1 COMPLEXITY THEORY CSci 5403 LECTURE XIII WHY...

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 Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 COMPLEXITY THEORY CSci 5403 LECTURE XIII: WHY CONSTANTS STILL DON’T MATTER RP = { A | exists polytime TM M: x 2 A ) Pr r [M(x,r) accepts] ¸ ½ x ∉ A ) Pr r [M(x,r) accepts] = 0. } coRP = { A | exists polytime TM M: x 2 A ) Pr r [M(x,r) accepts] = 1 x ∉ A ) Pr r [M(x,r) accepts] < ½ . } BPP = { A | exists polytime TM M: x 2 A ) Pr r [M(x,r) accepts] ¸ 2/3 x ∉ A ) Pr r [M(x,r) accepts] · 1/3. } Definition. A 2 ZPP if there exists PTM M so that 1. x 2 A ) M accepts x 2. x ∉ A ) M rejects x 3. For all x, the expected running time of M(x) is poly(|x|). Theorem. ZPP = RP Å coRP. Proof. A 2 RP \ coRP means 9 M, M’ : M(x) accepts ) x 2 A, Pr[M(x) accepts] ¸ ½ . M’(x) rejects ) x ∉ A, Pr[M’(x) rejects] ¸ ½ . while(true): run M(x). If M(x)=True: return True. run M’(x). If M’(x)=False: return False. Definition. A 2 ZPP if there exists PTM M so that 1. x 2 A ) M accepts x 2. x ∉ A ) M rejects x 3. For all x, the expected running time of M(x) is poly(|x|)....
View Full Document

{[ snackBarMessage ]}

Page1 / 4

lecture13 - 1 COMPLEXITY THEORY CSci 5403 LECTURE XIII WHY...

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