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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.

What is wi-fi infrastructure? a metropolitan area network that uses radio signals to transmit and receive data a communications technology aimed at providing high-speed wireless data over metropolitan area networks a means by which portable devices can connect wirelessly to a local area network, using access points that send and receive data via radio waves includes the inner workings of a wi-fi service or utility, including the signal transmitters, towers, or poles and additional equipment required to send out a wi-fi signal

Column a of irma’s spreadsheet contains titles for each row, but her document is too big and will be printed three pages across. she wants to be sure that every page will be understood. what can irma do to with this problem?