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’?
1
The pumping lemma for context-free languages states that for every CFL L there is a constant n such that every string z in L with \(|z| \ge n\) can be written as z = uvwxy satisfying three conditions.
Step 1 — \(|vwx| \le n\): the pumped part lies within a window of length n.
Step 2 — \(|vx| \ge 1\): at least one of v and x is non-empty, so pumping actually changes the string.
Step 3 — \(uv^i w x^i y \in L\) for every \(i \ge 0\).
If vx could have length 0, pumping would leave the string unchanged and the lemma would say nothing, so 0 is not allowed. Nothing forces vx to have length 2 or n: one pumped symbol is enough, and n is the upper bound on vwx, not a lower bound on vx.
1 option is correct.
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 ?
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 ?
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 ?
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 ?
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 ?
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 :
