pumping-lemma

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 $\Sigma=\{a, b, c\}$. For $x \in \Sigma^{\star}$, and $\alpha \in \Sigma$, let $\#_\alpha(x)$ denote the number of occurrences of a in $x$. Which one or more of the following o...

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 Σ = {a, b}, let us consider the regular language L = {x | x = a 2+3k or x = b 10+12k , k ≥ 0}. Which one of the following can be a pumping length (the constant guaranteed by th...

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} \...

Let $${L_1} = \left\{ {w \in \left\{ {0,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(110)'s$$ as $$(011)'s$$$$\left. \, \right\}$$. Let $${L_...

Let $${L_1} = \left\{ {w \in \left\{ {0,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(110)'s$$ as $$(011)'s$$$$\left. \, \right\}$$. Let $${L_...

Which one of the following is TRUE?

Which of the following is true for the language $$\left\{ {{a^p}} \right.\left| P \right.$$ prime $$\left. \, \right\}$$?

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...

If $$s$$ is a string over $${\left( {0 + 1} \right)^ * }$$ then let $${n_0}\left( s \right)$$ denote the number of $$0'$$ s in $$s$$ and $${n_1}\left( s \right)$$ the number of $$1...

Consider the following two statements; $${S_1}\,\,:\,\,\left\{ {{0^{2n}}\left| {n \ge 1} \right.} \right\}$$ is a regular language $${S_2}\,\,:\,\,\left\{ {{0^m}{1^n}{0^{m + n}}\le...

Consider the following languages: $${L_1} = \left\{ {w\,w\left| {w \in {{\left\{ {a,\,b} \right\}}^ * }} \right.} \right\}$$ $${L_2} = \left\{ {w\,{w^R}\left| {w \in {{\left\{ {a,\...

Which of the following sets can be recognized by a Deterministic Finite-state Automation?

Let $$L \subseteq \sum {^{^ * }\,} $$ where $$\,\sum { = \,\,\left\{ {a,b} \right\}\,\,} $$ which of the following is true?

Which of the following statements is / are true / false? The language $$\left\{ {{0^n}\,\left| {\,n} \right.} \right.$$ is prime$$\left. \, \right\}$$ is not regular