Pumping lemma constant, Theory of Computation

Assignment Help:

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.

Related Discussions:- Pumping lemma constant

Find a regular expression, Find a regular expression for the regular langua...

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

Chomsky normal form, s->0A0|1B1|BB A->C B->S|A C->S|null find useless symbo...

s->0A0|1B1|BB A->C B->S|A C->S|null find useless symbol?

Finite automata, design an automata for strings having exactly four 1''s

design an automata for strings having exactly four 1''s

Distinguish between mealy and moore machine, Distinguish between Mealy and ...

Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1's encountered is even or odd.

Kleene Closure, 1. Does above all''s properties can be used to prove a lang...

1. Does above all''s properties can be used to prove a language regular? 2..which of the properties can be used to prove a language regular and which of these not? 3..Identify one

Prism algorithm, what exactly is this and how is it implemented and how to ...

what exactly is this and how is it implemented and how to prove its correctness, completeness...

Prove the arden''s theorem, State and Prove the Arden's theorem for Regular...

State and Prove the Arden's theorem for Regular Expression

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd