A group of n people were removed from the hotel. After a month, the kidnappers need to get rid of these people, but they just don't want to let them go. They inform the hostages one evening that the next morning they will be lined up one behind the other so that everyone sees those in front of them but none behind. Then the captors will pass, starting with the last in line, and put a hat on everyone's head, either red or black. Hats put down, the kidnappers will come back, always starting at the end of the line, asking the simple question: what color hat do you have?. If the person gives the correct color, they will be released. Otherwise, it will be executed instantly. The only answer allowed (one that will not cause the responder to execute) is the color, black or red. (a) How many people can be saved and how? Explain in detail (a formal proof but not necessary at this time). (b) Give (draw) an AFD that models the rescue protocol, with its interpretation. Pay attention to the alphabet and the states. 2. Give a context-free grammar that generates the language L = {w {(,)} : w is parenthesis}. Prove your answer..