Let $$ < M > $$ be the encoding of a Turing machine as a string over $$\sum { = \left\{ {0,1} \right\}.} $$
Let $$L = \left\{ { < M > \left| M \right.} \right.$$ is a Turing machine that accepts a string of length $$\left. {2014} \right\}.$$ Then, $$L$$ is

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 $${L_2} = \left\{ {w \in \left\{ {0,\,\,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(000)'s$$ as $$(111)'s$$$$\left. \, \right\}$$. Which one of the following is TRUE?

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
$$\left. {\rm I} \right)$$ $$\,\,\,{L_{1 \bullet }}{L_2}$$ is a regular language
$$\left. {\rm II} \right)$$ $$\,\,\,{L_{1 \bullet }}{L_2} = \left\{ {{a^n}{b^n}\left| {n \ge \left. 0 \right\}} \right.} \right.$$
Which one of the following is CORRECT?

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 $${L_2} = \left\{ {w \in \left\{ {0,\,\,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(000)'s$$ as $$(111)'s$$$$\left. \, \right\}$$. Which one of the following is TRUE?