Closure Properties

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?

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 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...

Let $L_1, L_2$ be two regular languages and $L_3$ a language which is not regular. Which of the following statements is/are always TRUE?

Let $L_1, L_2$ be two regular languages and $L_3$ a language which is not regular. Which of the following statements is/are always TRUE?

Which of the following statements is/are CORRECT?

Which of the following statements is/are TRUE?

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?

Consider the following statements. I. If L 1 $$ \cup $$ L 2 is regular, then both L 1 and L 2 must be regular. II. The class of regular languages is closed under infinite union. Wh...

If L is a regular language over Σ = {a, b}, which one of the following languages is NOT regular?

The set of all recursively enumerable languages is

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 two statements : $$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ If all states of an $$NFA$$ are accepting states then the language accepted by the $$\,\,\,\,\,\,\,\,\,...

Consider the following types of languages: $${L_1}:$$ Regular, $${L_2}:$$ Context-free, $${L_3}:$$ Recursive, $${L_4}:$$ Recursively enumerable. Which of the following is/are TRUE...

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 statements. $$\,\,\,$$ $${\rm I}.\,\,\,\,\,\,\,\,\,$$ The complement of every Turing decidable language is Turing decidable $$\,$$ $${\rm II}.\,\,\,\,\,\,\,\...

If $${L_1} = \left\{ {{a^n}\left| {n \ge \left. 0 \right\}} \right.} \right.$$ and $${L_2} = \left\{ {{b^n}\left| {n \ge \left. 0 \right\}} \right.} \right.,$$ consider $$\left. {\...

Which of the following statements is/are FALSE ? $$1.$$ For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine $$2.$$ Turing recognizab...

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.}...

Which of the following problems are decidable? $$1.$$ Does a given program ever produce an output? $$2.$$ If L is a context-free language, then, is $$\overline L $$ also context-fr...

Let $${L_1}$$ recursive language. Let $${L_2}$$ and $${L_3}$$ be languages that are recursively enumerable but not recursive. Which of the following statement is not necessarily tr...

For $$s \in {\left( {0 + 1} \right)^ * },$$ let $$d(s)$$ denote the decimal value of $$s(e. g.d(101)=5)$$ Let $$L = \left\{ {s \in {{\left( {0 + 1} \right)}^ * }\left| {\,d\left( s...

Let $${L_1}$$ be a regular language, $${L_2}$$ be a deterministic context-free language and $${L_3}$$ a recursively enumerable, but not recursive, language. Which one of the follow...

Let $${L_1}$$ be a recursive language, and Let $${L_2}$$ be a recursively enumerable but not a recursive language. Which one of the following is TRUE?

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?

Context free languages are closed under:

If $${L_1}$$ is a context free language and $${L_2}$$ is a regular which of the following is/are false?

Which of the following statements is false?

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?

Given that language $${L_1}$$ is regular and that the language $${L_1} \cap {L_2}$$ is regular is the language $${L_2}$$ is always regular?

Which of the following statements is / are true / false? Union of two recursive languages is recursive

Which of the following statements is / are true / false? Regular languages are closed under infinite union.

State whether the following statement is TRUE / FALSE. Regularity is preserved under the operation of string reversal.

State whether the following statement is TRUE / FALSE. The intersection of two $$CFL's$$ is also $$CFL.$$

Let $${R_1}$$ and $${R_2}$$ be regular sets defined over the alphabet $$\sum \, $$ then:

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

Is the class of regular sets closed under infinite union? Explain.