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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.

Using least squares fitting, you are to fit the data sets to the following models and solve for the parameters ai , where i is the index of the parameter. the input/output data for the systems are linked in the bblearn site. for each of the systems use matlab to plot the supplied data vs. the model fit on one plot. include your code in the solutions. (a) linear fit "lineardata.mat" y=a1x^3 + a2x^2 + a3x + a4 (b) plant fit "plantdata.mat g(s) = a1/(s + a2)

The program below has been generalized to read a user's input value for hourlywage. run the program. notice the user's input value of 10 is used. modify that input value, and run again. generalize the program to get user input values for workhoursperweek and workweeksperyear (change those variables' initializations to 0). run the program. monthsperyear will never change, so define that variable as final. use the standard for naming final variables. ex: final int max_length