CS 334 Fall 2018: Problem Set 1. Problem 1(10 points) Construct deterministic FSAs for each of the following languages over the alphabet ta, bj: 1. L (w:w contains the string aaa or the string bbb) 2. L2 [w: w contains the string aaa and the string bbb) Problem 2. (10 points) With the soccer season upon us, you have been selected to design the finite state controller for scoring penalty shootouts. The rules for a penalty shootout are as follows: 1. In every round the visitors shoot first, followed by the home team. Each goal scored earns one point If, at the end of 5 rounds the teams are tied then more rounds are played. 3. 2. The game ends as soon as at least 5 rounds have been played and the scores are different at the end of the last round played. 4. The team with more total points at the end wins the game. Design an FSA for scoring penalty shootouts. The FSA must accept shootouts corresponding to a win for the home team (presumably to set off the fireworks display) and reject all non- winning plays. Be sure to specify all components of your FSA in detail. Problem 3. (10 points) Modify the proof of Theorem 1.25 in the textbook to cover the case