43 Slides--Context-Free Languages

43 Slides--Context-Free Languages - CS103 HO#43...

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

View Full Document Right Arrow Icon
CS103 HO#43 Slides--Context-Free Languages 5/10/10 1 The Pumping Lemma If A is a regular language, then there is a number p (the pumping length) such that, if s is any string in A of length at least p , then s may be divided into three pieces, s = xyz satisfying the following three conditions: 1. for each i 0, xy i z A, 2. |y| > 0, and 3. |xy| p. FOR ANY regular language A, THERE EXISTS a number p such that FOR ANY string s in A with |s| p THERE EXIST strings x, y, z, such that s = xyz and … The Pumping Lemma If A is a regular language, then there is a number p (the pumping length) such that, if s is any string in A of length at least p , then s may be divided into three pieces, s = xyz satisfying the following three conditions: 1. for each i 0, xy i z A, 2. |y| > 0, and 3. |xy| p. To show that language A is NOT REGULAR , assume it is and get a contradiction from this FOR ANY regular language A, THERE EXISTS a number p such that FOR ANY string s in A with |s| p THERE EXIST strings x, y, z, such that s = xyz and . .. The Pumping Lemma If A is a regular language, then there is a number p (the pumping length) such that, if s is any string in A of length at least p , then s may be divided into three pieces, s = xyz satisfying the following three conditions: 1. for each i 0, xy i z A, 2. |y| > 0, and 3. |xy| p. To show that language A is NOT REGULAR , assume it is and get a contradiction. If A is regular, there is a pumping length p that works for any s where |s| p. Given p, show how to find an s of sufficient length that cannot be pumped. That is, no matter how we divide s in to xyz there is an i such that xy i z A. (This may involve analyzing several cases.) FOR ANY regular language A, THERE EXISTS a number p such that FOR SOME string s in A with |s| p FOR ALL strings x, y, z, such that s = xyz and . .. Show that L = { w | w { ) , ( }* and w has balanced parentheses } is not regular.
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.

This document was uploaded on 02/08/2011.

Page1 / 4

43 Slides--Context-Free Languages - CS103 HO#43...

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