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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.

In this lab, you complete a prewritten c++ program for a carpenter who creates personalized house signs. the program is supposed to compute the price of any sign a customer orders, based on the following facts: the charge for all signs is a minimum of $35.00. the first five letters or numbers are included in the minimum charge; there is a $4 charge for each additional character. if the sign is made of oak, add $20.00. no charge is added for pine. black or white characters are included in the minimum charge; there is an additional $15 charge for gold-leaf lettering. instructions ensure the file named housesign. cppis open in the code editor. you need to declare variables for the following, and initialize them where specified: a variable for the cost of the sign initialized to 0.00 (charge). a variable for the number of characters initialized to 8 (numchars). a variable for the color of the characters initialized to "gold" (color). a variable for the wood type initialized to "oak" (woodtype). write the rest of the program using assignment statements and ifstatements as appropriate. the output statements are written for you. execute the program by clicking the run button. your output should be: the charge for this sign is $82. this is the code, // housesign. cpp - this program calculates prices for custom made signs. #include #include using namespace std; int main() { // this is the work done in the housekeeping() function // declare and initialize variables here // charge for this sign // color of characters in sign // number of characters in sign // type of wood // this is the work done in the detailloop() function // write assignment and if statements here // this is the work done in the endofjob() function // output charge for this sign cout < < "the charge for this sign is $" < < charge < < endl; return(0); }

How do you take a green screen out of the video while editing?