Q4. Consider the children's game Rock, Paper, Scissors. We'll say that the first player to win two rounds wins the game. Call the two players A and B.
a) Define an alphabet and describe a technique for encoding Rock, Paper, Scissors games as strings over . (Hint: each symbol in should correspond to an ordered pair that describes the simultaneous actions of A and B.)
b) Let LRPS be the language of Rock, Paper, Scissors games, encoded as strings as described in part (a), that correspond to wins for player A. Show a DFSM that accepts LRPS.