4. Determine which of the following formule are satisfiable: S. a) Let A be a DFA with m states. Argue that all useful" states (the states that can be reached with some input string) can be reached with input strings whose lengths are m -1 or less. b) Devise a Turing machine that determines if an arbitrary DFA rejects any strings, i.e., a TM that decides on A) | A is a DFA that rejects some string c) Analyze the time complexity of your Turing machine and determine if it is in P