Given a sequence of values a1, . . , an give an algorithm that finds the coefficients of the polynomial p(x) of degree n such that p(x) = 0 if and only if x = ai for some i. you can assume the elements ai are distinct. your algorithm should run in time o(n log2 n).

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.

Acetylene is a gas which burns rapidly on its own, and is considered highly explosive. a) true b) false

Arecipients list has been loaded into a document. which commands should be clicked in order to filter the list so that letters will not be printed for recipients who live in a certain state? mailings tab, start mail merge, select recipients, type new list, then insert only contacts from the desired states mailings tab, rules, select recipients, use existing list, then choose a recipients list that includes only contacts in certain states mailings tab, select recipients, use existing list, rules, fill in, then type in certain states mailings tab, rules, skip record select “state” under field name, then type in the state name under “equal to”