49+Slides--Complexity (1)

# 49+Slides--Complexity (1) - CS103 HO#49 Slides-Complexity...

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

CS103 HO#49 Slides--Complexity 11/12/10 1 Mapping Reducibility w A f(w) B. w A f(w) B f(w) B w A f(w) B w A w A f(w) B Note that A M B A M B AB f Mapping Reducibility Theorem 5.22: If A M B and B is decidable, then A is decidable. recognizable recognizable Corollary 5.23: If A M B and A is undecidable, then B is undecidable. not recognizable not recognizable maps to A B ¬ Solvable(A) ¬ Solvable(B) A language known not to be decidable A language whose decidability we are trying to determine If B decidable Then A decidable But A not decidable So B not decidable A m B Using Mapping Reductions: The Most Common Scenario Using Mapping Reductions: A Less Common Scenario maps to A B A language known to be decidable A language whose decidability we are trying to determine A m B Solvable(B) Solvable(A) If B decidable Then A decidable E TM = { M | L(M) = Ø} (accepts nothing) NE TM ={ M | L(M) Ø} (accepts something) NE TM is Turing-recognizable Build a non-deterministic TM M' : M Guess w w Simulate M on w Accepts w Accept M M' If M accepts any string, M' will guess it, and M' accepts M . If L(M) = Ø, no guess leads to acceptance, so M' does not accept M. So L( M' ) = NE TM Big-O Notation • The exact running time of an algorithm may be a complicated function of the length of its input, so we typically just estimate it. • The question we generally ask is: how does the running time of an algorithm change as we size of the input gets very large. This is called asymptotic analysis.

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

View Full Document
CS103 HO#49 Slides--Complexity 11/12/10 2 Big-O Notation Let f and g be functions f, g: N R + . We say that f(n) = O(g(n)) if there are positive integers c and n 0 such that for every integer n > n 0 f(n) c g(n).
This is the end of the preview. Sign up to access the rest of the document.

## This document was uploaded on 02/08/2011.

### Page1 / 4

49+Slides--Complexity (1) - CS103 HO#49 Slides-Complexity...

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

View Full Document
Ask a homework question - tutors are online