Consider the following problem $$X.$$ Given a Turing machine $$M$$ over the input alphabet $$\sum , $$ any state $$q$$ of $$M$$ And a word $$w\,\,\varepsilon \,\,\sum {^ * ,} $$ does the computation of $$M$$ on $$w$$ visit the state $$q''$$

Which of the following statements about $$X$$ is correct?

Consider the following decision problems :

$${P_1}$$ Does a given finite state machine accept a given string

$${P_2}$$ Does a given context free grammar generate an infinite number of stings.

Which of the following statements is true?

Which one of the following is the strongest correct statement about a finite language over some finite alphabet $$\sum ? $$

It is decidable whether: