Consider three decision problems $${P_1},$$ $${P_2}$$ and $${P_3}.$$ It is known that $${P_1}$$ is decidable and $${P_2}$$ is un-decidable. Which of the following is TRUE?

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 $$\sum ? $$