Given the following two languages : \(L_{1} = \{a^{n}\, b\, a^{n} \mid n \gt 0\}\) \(L_{2} = \{a^{n}\, b\, a^{n}\, b^{n+1} \mid n \gt 0\}\) Which of the following is correct ?
\(L_{1}\) is context free language and \(L_{2}\) is not context free language
\(L_{1}\) needs one matching of the a's before and after b; the grammar \(S \to aSa \mid aba\) generates it, so it is context free.
\(L_{2}\) needs three blocks to agree in size (a's, a's and b's), which a single stack cannot track; pumping a string \(a^{p}ba^{p}b^{p+1}\) breaks the equality, so it is not context free.
So only the first language is context free.
Hence, \(L_{1}\) is context free language and \(L_{2}\) is not context free language.
Similar Questions
According to pumping lemma for context free languages :
Let L be an infinite context free language, then there exists some positive integer m such that any \(w \in L\) with \(|w| \ge m\) can be decomposed as \(w = uvxyz\)
Consider a language A defined over the alphabet \(\Sigma = \{0, 1\}\) as \(A = \left\{0^{\lfloor n/2 \rfloor} 1^{n} : n \gt = 0\right\}\).
The expression \(\lfloor n/2 \rfloor\) means the floor of n/2, or what you get by rounding n/2 down to the nearest integer.
Which of the following is not an example of a string in A ?
Which of the following are context free language ?
(A) {wi xj yk zl | i + k = j + l, where i, j, k, l ≥ 0}
(B) {wi xj yk zl | i = j and k = l, where i, j, k, l ≥ 0}
(C) {wi xj yk zl | i = j = k and k ≠ l, where i, j, k, l ≥ 0}
(D) {wi xj yk zl | i = j = k + l, where i, j, k, l ≥ 0}
(E) {wi xj yk zl | i = j = l and k ≠ l, where i, j, k, l ≥ 0}
Choose the correct answer from the options given below :
If L1 and L2 are context free languages, which of the following is True about L1∩L2 ?
In Pumping Lemma for context free languages, to say a language is satisfying pumping lemma, what is the minimum length of ‘vx’ together, if you consider the string as ‘uvwxy’?
Let L = {0n1n|n ≥ 0} be a context free language.
Which of the following is correct ?
Given the following two statements :
A. L = {w|na(w) = nb(w)} is deterministic context free language, but not linear.
B. L = {an bn} ∪ {an b2n} is linear, but not deterministic context free language.
Which of the following options is correct ?
Given the following two languages :
L1 = {an bn | n ≥ 0, n ≠ 100}
L2 = {w ∈ {a, b, c}*| na(w) = nb(w) = nc(w)}
Which of the following options is correct ?
Important Questions from Context Free Languages
- Let $\Sigma = \{a, b, c, d\}$ and let $L = \{a^ib^jc^kd^\ell \mid i, j, k, \ell \ge 0\}$.
Which of the following constraints ensure(s) that the language $L$ is context-free? According to pumping lemma for context free languages :
Let L be an infinite context free language, then there exists some positive integer m such that any \(w \in L\) with \(|w| \ge m\) can be decomposed as \(w = uvxyz\)
Consider a language A defined over the alphabet \(\Sigma = \{0, 1\}\) as \(A = \left\{0^{\lfloor n/2 \rfloor} 1^{n} : n \gt = 0\right\}\).
The expression \(\lfloor n/2 \rfloor\) means the floor of n/2, or what you get by rounding n/2 down to the nearest integer.
Which of the following is not an example of a string in A ?
Which of the following are context free language ?
(A) {wi xj yk zl | i + k = j + l, where i, j, k, l ≥ 0}
(B) {wi xj yk zl | i = j and k = l, where i, j, k, l ≥ 0}
(C) {wi xj yk zl | i = j = k and k ≠ l, where i, j, k, l ≥ 0}
(D) {wi xj yk zl | i = j = k + l, where i, j, k, l ≥ 0}
(E) {wi xj yk zl | i = j = l and k ≠ l, where i, j, k, l ≥ 0}
Choose the correct answer from the options given below :
If L1 and L2 are context free languages, which of the following is True about L1∩L2 ?
