Consider idealized versions of two U. S. professional sports. In football, a team can score 2,3, or 6 points at a time. Having scored 6 points, it can then score an additional 0, 1, or 2 points. In baseball, runs (points) occur one at a time. However, if a game ends with each team having the same number of runs, an additional inning is played to resolve the tie. (This rule is applied recursively.) We assume, somewhat unrealistically, that there is no upper limit to the scores for either game. Required:
a. Give a regular expression for the set of possible football scores: m–n, with m and n in unary notation.
b. Give an NFA for the same language.
c. Same as b), but now give a DFA.
d. Show that the set of possible baseball scores is not regular.