Problem 2.3 [40 points] Purpose: Synthesize deterministic finite automata. Draw state diagrams of DFAs accepting the following language over {0,1}*. a. {w w begins with a 1 and ends with a 0} b. {w w contains at least three 1's} C. {w w contains the substring 0101, that is w=x0101y for strings x and y} d. {w w has length at least three and its third symbol is a 0} e. {w w starts with O and has odd length, or starts with 1 and has even length} f. {w w does not contain the substring 110} g. {w the length of wis at most 5} h. {w w is any string except 11 and 111} i. {w every odd position of wis a 1}, e.g., 101 is in the language j. {w w contains at least two o's and at most one 1} k. {e, 0), where e denotes the empty string 1. { ww contains an even number of o's, or exactly two 1's} m. The empty set n. All strings except the empty string. You can think of these as little routines, so to check your answers, try them in cases you know what the results (accept/reject) should be, edge cases like the empty string, etc