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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.

Consider how gaming consoles initially relied on joysticks and joypads and then made the switch to modern gaming controls, which include analog sticks, buttons and switches, touch controls, accelerometers, motion controls, etc. name at least two kinds of gaming experiences that are possible with these new control devices but were not possible on original joysticks. explain how new technologies made this newer game style possible.

Type the correct answer in the box. spell all words correctly. under which key category do the page up and page down keys fall? page up and page down keys fall under the keys category.