Which of the following is/are undecidable?
For a Turing machine M, {M} denotes an encoding of M. Consider the following two languages.
L1 = {(M) | M takes more than 2021 steps on all inputs}
L2 = {(M) | M takes more than 2021 steps on some input}
Which one of the following options is correct?
$$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ 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?