Consider the following decision problems:
$(P1):$ Does a given finite state machine accept a given string?
$(P2):$ Does a given context free grammar generate an infinite number of strings?
Which of the following statements is true?
- Both$(P1)$ and $(P2)$ are decidable
- Neither $(P1)$ nor $(P2)$ is decidable
- Only $(P1)$ is decidable
- Only $(P2)$ is decidable