Regular_Pumping_Examples

# Regular_Pumping_Examples - MoreApplications of...

This preview shows pages 1–8. Sign up to view the full content.

More Applications  of the Pumping Lemma

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

View Full Document
The Pumping Lemma:  Given a infinite regular language  L  there exists an integer        (critical length) m  for any string              with length    L w m w | |  we can write z y x w =  with                        and m y x | | 1 | | y  such that: L z y x i ... , 2 , 1 , 0 = i
Regular languages Non-regular languages *} : { Σ = v vv L R

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

View Full Document
Theorem: The language is not regular Proof: Use the Pumping Lemma *} : { Σ = v vv L R } , { b a = Σ
Assume for  contradiction that       is a regular language L Since        is  infinite we can apply the  Pumping Lemma   L *} : { Σ = v vv L R

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

View Full Document
m m m m a b b a w =  We pick Let        be the critical length for Pick  a string       such that:   w L w m w | | length m and *} : { Σ = v vv L R L
we can write: z y x a b b a w m m m m = = with lengths:

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/02/2011 for the course AR 107 taught by Professor Gracegraham during the Fall '11 term at Montgomery College.

### Page1 / 31

Regular_Pumping_Examples - MoreApplications of...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online