context-free languages

Let $L_1$ and $L_2$ be two languages over a finite alphabet, such that $L_1 \cap L_2$ and $L_2$ are regular languages. Which of the following statements is/are always true?

Let $\Sigma=\{a, b, c, d\}$ and let $L=\left\{a^i b^j c^k d^l \mid i, j, k, l \geq 0\right\}$. Which of the following constraints ensure(s) that the language $L$ is context-free?

Consider the two lists List I and List II given below: List I (i) Context free languages (ii) Recursive languages (iii) Regular languages List II (a) Closed under union (b) Not clo...

Consider the following two languages over the alphabet {a, b, c}, where m and n are natural numbers. L₁ = {a^m b^m c^(m+n) | m, n ≥ 1} L₂ = {a^m b^n c^(m+n) | m, n ≥ 1} Which ONE o...

Consider the following two languages over the alphabet $\{a, b, c\}$, where $m$ and $n$ are natural numbers. $$\begin{aligned} & L_1=\left\{a^m b^m c^{m+n} \mid m, n \geq 1\right\}...

Let $G_1, G_2$ be Context Free Grammars (CFGs) and $R$ be a regular expression. For a grammar $G$, let $L(G)$ denote the language generated by $G$. Which ONE among the following qu...

Consider the two lists List-I and List-II given below: List - I List - II (i) Context free languages (a) Closed under union (ii) Recursive languages (b) Not closed under complement...

Which of the following statements is/are CORRECT?

Consider the following languages: $$\eqalign{ & {L_1} = \{ ww|w \in \{ a,b\} *\} \cr & {L_2} = \{ {a^n}{b^n}{c^m}|m,\,n \ge 0\} \cr & {L_3} = \{ {a^m}{b^n}{c^n}|m,\,n \ge 0\} \cr}...

For a string w, we define w R to be the reverse of w. For example, if w = 01101 then w R = 10110. Which of the following languages is/are context-free?

Let L 1 be a regular language and L 2 be a context-free language. Which of the following languages is/are context-free?

Suppose that L 1 is a regular and L 2 is a context-free language, Which one of the following languages is NOT necessarily context-free?

Which one of the following languages over $\Sigma=\{a, b\}$ is NOT context-free?

Consider the following languages: $$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m + p = n + q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$ $$\...

Let L1, L2 be any two context-free languages and R be any regular language. Then which of the following is/are CORRECT? I. L₁ U L₂ is context-free. II. L₁ is context-free. III. L₁...

Consider the following languages : $$$\eqalign{ & {L_1} = \left\{ {{a^n}{b^m}{c^{n + m}}:m,n \ge 1} \right\} \cr & {L_2} = \left\{ {{a^n}{b^n}{c^{2n}}:n \ge 1} \right\} \cr} $$$ Wh...

Which of the following languages are context-free? $$$\eqalign{ & {L_1} = \left\{ {{a^m}{b^n}{a^n}{b^m}|m,n \ge 1} \right\} \cr & {L_2} = \left\{ {{a^m}{b^n}{a^m}{b^n}|m,n \ge 1} \...

For any two languages L 1 and L 2 such that L 1 is context-free and L 2 is recursively enumerable but not recursive, which of the following is/are necessarily true? I. $${\overline...

Consider the following languages $${L_1} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0} \right.} \right\}$$ $${L_2} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0,p \ne r} \right.}...

Consider the languages $$$\eqalign{ & {L_1} = \left\{ {{0^i}{1^j}\,\left| {i \ne j} \right.} \right\},\,{L_2} = \left\{ {{0^i}{1^j}\,\left| {i = j} \right.} \right\}, \cr & {L_3} =...

Which of the following are decidable? $$1.$$ Whether the intersection of two regular languages is infinite $$2.$$ Whether a given context-free language is regular $$3.$$ Whether tw...

Let $${L_1} = \left\{ {{0^{n + m}}{1^n}{0^m}\left| {n,m \ge 0} \right.} \right\},$$ $$\,\,\,{L_2} = \left\{ {{0^{n + m}}{1^{n + m}}{0^m}\left| {n,m \ge 0} \right.} \right\},$$ and...

Consider the language : $${L_1} = \left\{ {{a^n}{b^n}{c^m}\left| {n,m > 0} \right.} \right\}$$ and $${L_2} = \left\{ {{a^n}{b^m}{c^m}\left| {n,m > 0} \right.} \right\}$$ Which of t...

Which of the following is true?

Which of the following statement is true?

Let $${L_D}$$ be the set of all languages accepted by a $$PDA$$ by final state and $${L_E}$$ the set of all languages accepted by empty stack. Which of the following is true?

Context free languages are closed under:

If $${L_1}$$ and $${L_2}$$ are context free languages and $$R$$ a regular set, one of the languages below is not necessarily a context free language. Which one?

Context free languages and regular languages are both closed under the operation(s) of :