A location where you can store files

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.

The reset circuit used on the four 3-bit counters analyzed in this activity reset the counts to zero (000). it makes sense for the up-counters to start at zero (000), but the down-counters should start at seven (111). what would you need to change so that the 3-bit binary down counter with j/k flip-flops you just created would reset to seven (111)?

Amitha writes up a one-page summary of a novel during her summer internship at a publishing company. when she reads over the page, she realizes she used the word “foreshadow” seven times, and she would like to reduce the repetition. which tool would best amitha solve this problem?