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Your task this week is to write a very simple spam classifier in python. it will classify messages as either spam (unwanted) or ham (wanted). the program will have a set of spam_words, words that are known to appear in spam messages. that set is included in the template file spam. pypreview the document. you will also define a spam threshold which reflects the allowed percentage of spam words in the message. you'll compute a 'spam indicator', which is the ratio of spam words to the total number of unique words in the message. if the spam indicator exceeds the spam threshold, the message is classified as spam. otherwise it is classified as ham. we'll assume that the spam threshold is a constant and has a value of 0.10. your program will prompt the user for a message and then will print the corresponding spam indicator with two decimal digits and the corresponding classification (spam or ham). the program will be case insensitive. the spam words are detected whether they are in lower case or upper case or mixed case. each word, spam or not, is counted once (even if it appears multiple times in the message.) the program will remove punctuation from the message before identifying the words and computing the spam indicator. for example '! ' must be identified as the spam word 'now'.

4.11 painting a wall (1) prompt the user to input integers for a wall's height and width. calculate and output the wall's area (integer). note that in this case there is a new line after each prompt. (submit for 1 point). enter wall height (feet): 11 enter wall width (feet): 15 wall area: 165 square feet (2) extend to also calculate and output the amount of paint in gallons needed to paint the wall (floating point). assume a gallon of paint covers 350 square feet. store this value in a variable. output the amount of paint needed using the %f conversion specifier. (submit for 2 points, so 3 points total). enter wall height (feet): 11 enter wall width (feet): 15 wall area: 165 square feet paint needed: 0.471429 gallons (3) extend to also calculate and output the number of 1 gallon cans needed to paint the wall. hint: use a math function to round up to the nearest gallon. (submit for 2 points, so 5 points total). enter wall height (feet): 11 enter wall width (feet): 15 wall area: 165 square feet paint needed: 0.471429 gallons

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.