Question

In: Computer Science

Prove that {anbamba2m+n:n,m≥1} is not regular using pumping lemma

Prove that {anbamba2m+n:n,m≥1} is not regular using pumping lemma

Solutions

Expert Solution

To prove that is not regular, use the pumping lemma for regular languages as follows.

Let the pumping length be . Consider the word which has length at least p, which is in the language as per the definition of the language with .

Consider any breakup of the word . Then xy must consist of only 'a's from the first block, otherwise it's length will exceed p. Hence . Now consider the pumped down word . Then this word has , but the number of 'a's in the last block is . As , this means , hence . This means that the word w' doesn't satisfy the property to be in the language, hence .

This proves the language is not regular using the pumping lemma for regular language. Comment in case of any doubts.

venereology answered 11 months ago
Next > < Previous

Related Solutions

Prove that the following language are NOT regular using the pumping lemma (20 pt.) ? =...
Prove that the following language are NOT regular using the pumping lemma (20 pt.) ? = {? ∈ {?, #}∗ | ? = ??#??# ... #?? ??? ? ≥ ?, ?? ∈ ?∗ ??? ????? ?, ??? ?? ≠?? ???????? ?≠?} Hint: choose a string ? ∈ ? that contains ? #’s.
(35 pt.) Prove that the following languages are not regular using the pumping lemma. (15pt.)?={?????? |?,?≥?}...
(35 pt.) Prove that the following languages are not regular using the pumping lemma. (15pt.)?={?????? |?,?≥?} (20 pt.) ? = {? ∈ {?, #}∗ | ? = ??#??# ... #?? ??? ? ≥ ?, ?? ∈ ?∗ ??? ????? ?, ??? ?? ≠?? ???????? ?≠?} Hint: choose a string ? ∈ ? that contains ? #’s.
1. Pumping Lemma: a. Is the following language a regular language? (Use pumping lemma in proof.)...
1. Pumping Lemma: a. Is the following language a regular language? (Use pumping lemma in proof.) L = {0n 1n 2n | n ≥ 0} b. What is (i.e., define) the CFL pumping lemma?
Use the pumping lemma to prove that the following languages are not regular. (a)L2 = {y...
Use the pumping lemma to prove that the following languages are not regular. (a)L2 = {y = 10 × x | x and y are binary integers with no leading 0s, and y is two times x}. (The alphabet for this languages is {0, 1, ×, =}.) For example, 1010 = 10 × 101 is in L2, but 1010 = 10 × 1 is not. (b)Let Σ2 = {[ 0 0 ] , [ 0 1 ] , [ 1...
Using the pumping lemma, prove that the language {1^n | n is a prime number} is...
Using the pumping lemma, prove that the language {1^n | n is a prime number} is not regular.
Do not use Pumping Lemma for Regular Expression to prove the following. You may think of...
Do not use Pumping Lemma for Regular Expression to prove the following. You may think of Closure Properties of Regular Languages 1. Fix an alphabet. For any string w with |w| ≥ 2, let middle(w) be the string obtained by removing the first and last symbols of w. That is, Given L, a regular language on Σ, prove that f1(L) is regular, where f1(L) = {w : middle(w) ∈ L}
Using the pumping lemma for regular languages, show that language is not regular. b) L3= {0n...
Using the pumping lemma for regular languages, show that language is not regular. b) L3= {0n 1m, m = n+2 } Language= {0,1}
In pumping lemma I know how to prove 0^n 1^n is not regular but what changes...
In pumping lemma I know how to prove 0^n 1^n is not regular but what changes when I have 0^n 1^n 2^n (three variables). Do I need to check 6 variations of 0,1 and 2 instead of only 3 in 0^n 1^n? thanks.
Use the Pumping Lemma to show that the following languages are not regular. (a) {ai bj...
Use the Pumping Lemma to show that the following languages are not regular. (a) {ai bj | i > j} (b) {apaq | for all integers p and q where q is a prime number and p is not prime}.
Use the pumping lemma to show that the following languages are not regular. A a. A1={0^n...
Use the pumping lemma to show that the following languages are not regular. A a. A1={0^n 1^n 2^n | n≥0} b. A2 = {www | w ∈ {a,b}∗} A c. A3 ={a^2^n | n≥0} (Here, a^2^n means a string of 2^n a’s.) A ={a3n |n > 0 }
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT