Consider the following problems. $$L(G)$$ denotes the language generated by a grammar $$G.$$ $$L(M)$$ denotes the language accepted by a machine $$M.$$

$$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ For an unrestricted grammar $$G$$ and a string $$W,$$ whether $$w \in L\left( G \right)$$
$$\,\,\,\,\,\,{\rm II}.\,\,\,\,\,\,\,$$ Given a Turing machine $$M,$$ whether $$L(M)$$ is regular
$$\,\,\,\,{\rm III}.\,\,\,\,\,\,\,$$ Given two grammars $${G_1}$$ and $${G_2}$$, whether $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)$$
$$\,\,\,\,{\rm IV}.\,\,\,\,\,\,\,$$ Given an $$NFA$$ $$N,$$ whether there is a deterministic $$PDA$$ $$P$$ such that $$N$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$\,\,\,\,\,\,\,\\,\,\,$$and $$P$$ accept the same language.

Which one of the following statements is correct?

Consider the following languages.

$$\,\,\,\,\,\,\,\,\,\,\,\,$$ $${L_1} = \left\{ {\left\langle M \right\rangle |M} \right.$$ takes at least $$2016$$ steps on some input $$\left. \, \right\},$$
$$\,\,\,\,\,\,\,\,\,\,\,\,$$ $${L_2} = \left\{ {\left\langle M \right\rangle |M} \right.$$ takes at least $$2016$$ steps on all inputs $$\left. \, \right\}$$ and
$$\,\,\,\,\,\,\,\,\,\,\,\,$$ $${L_3} = \left\{ {\left\langle M \right\rangle |M} \right.$$ accepts $$\left. \varepsilon \right\},$$

where for each Turing machine $${M,\left\langle M \right\rangle }$$ denotes a specific encoding of $$M.$$ Which one of the following is TRUE?

Let $$X$$ be a recursive language and $$Y$$ be a recursively enumerable but not recursive language. Let $$W$$ and $$Z$$ be two languages such that $$\overline Y $$ reduces to $$W,$$ and $$Z$$ reduces to $$\overline X $$ (reduction means the standard many-one reduction). Which one of the following statements is TRUE?

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