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Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

3. (5 points) describe what would be printed by the code below or what error would occur. const char* cstr = "0123456"; const char* ptr = & cstr[4]; cout < < ptr[-1] < < ptr < < endl; 1 4. (5 points) theseus has been trapped in a maze with a minotaur, which is trying to capture him. each round, theseus and the minotaur move through the maze; theseus towards the exit, and the minotaur towards theseus. theseus can move in any of the four cardinal directions, or he can wait for a round to see how the minotaur moves. write code that creates a data type to represent the possible moves that theseus could make.

Events and conditions that happen within an organization that are somewhat easier to deal with when responding to change are called