Pumping lemma constant, Theory of Computation

a) Let n be the pumping lemma constant. Then if L is regular, PL implies that s can be decomposed into xyz, |y| > 0, |xy| ≤n, such that xy i z is in L for all i ≥0.

Since the length of xy ≤n, y consists of all b's Then xy 2 z = anbncn, where the length of of y = j. We know j > 0 so the length of the pumped string contains at as many a's as b's as c's, and is not in L. This is a Contradiction L = {w :| n a (w) = n b (w) = nc(w)}

b)

  • Let n be the pumping lemma constant. Then if L is regular, PL implies that s = anbncm can be decomposed into xyz, |y| > 0, |xy| ≤n, such thatxy i z is in L for all i ≥0.
  • Since the length of xy ≤n, there are three ways to partition s:

1. y consists of all a's

Pumping y will lead to a string with more than n a's -- not in L

2. y consists of all b's

Pumping y will lead to a string with more than m b's, and leave

the number of c's untouched, such that there are no longer 2n more c's than b's -- not in L

3. y consists of a's and b's

Pumping y will lead to a string with b's before a's, -- not in L

  • There is no way to partition anbncm that pumped strings are still in L.
Posted Date: 2/23/2013 12:53:05 AM | Location : United States







Related Discussions:- Pumping lemma constant, Assignment Help, Ask Question on Pumping lemma constant, Get Answer, Expert's Help, Pumping lemma constant Discussions

Write discussion on Pumping lemma constant
Your posts are moderated
Related Questions

https://www.google.com/search?q=The+fomula+n%3D%28x%3D0%29%2F%281%3D2%29.The+value+x%3D0+and+is+used+to+stop+the+algerithin.The+calculation+is+reapeated+using+values+of+x%3D0+is+in

how to convert a grammar into GNF

De?nition Instantaneous Description of an FSA: An instantaneous description (ID) of a FSA A = (Q,Σ, T, q 0 , F) is a pair (q,w) ∈ Q×Σ* , where q the current state and w is the p


Prepare the consolidated financial statements for the year ended 30 June 2011. On 1 July 2006, Mark Ltd acquired all the share capitall of john Ltd for $700,000. At the date , J

Find a regular expression for the regular language L={w | w is decimal notation for an integer that is a multiple of 4}

Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about