1. Give state diagrams of DFAs with as few states as you can recognizing the following languages.

L₄ = {w | w represents a possible series of flips in the game in which player 1 wins where H represents heads and T represents tails} where the game goes like this: Repeatedly flip a coin. On heads, player 1 gets a point. On tails, player 2 gets a point. A player wins (and the game ends) as soon as they are ahead by two points.