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..
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A group of n people were removed from the hotel After a mon.pdf
1. 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.
