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LETTT RAI

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.

Sam is a data analyst at an advertising firm. he often uses a spreadsheet that contains media ratings details. he would like to filter the spreadsheet data based on different filter criteria. which operators can he use to specify the combination of filter criteria? sam can use the ( blank ) operators to specify a combination of filter criteria.

Aconstruction company is creating a powerpoint presentation describing how they calculate costs during each construction step. they plan to email this presentation to clients. the individual clients will be watching the presentation slide show on their own personal computers. what is the most important formatting step the company should take to make the text readable and pleasing to the eye?