In this assignment you'll design and implement a DFA (Deterministic Finite State Automaton). Let ={a,b,c,,z} be the alphabet of lower case characters. Pick the name (first and last name) of any group member. Let L be the regular language of all character sequences that contain the first name and last that order as substrings (with the names in lower case omitting any special characters). Before, between, and after the names there may be arbitrary many (including 0) arbitrary characters. 1. Write L as a regular expression. 2. Draw the graph of a DFA M=(Q,,,q0,F) that recognizes L. 3. Implement the DFA M in your favorite programming language: A. Your program should read input characters one by one and update its current state as specified by the DFA M. B. Once the input string has been read completely the program should check the current state and report "accept" or "reject". C. You should implement the transition function :QQ and then use it in a loop. In each iteration one character will be read and will be called to the current state. D. Demonstrate that your program works by running it on some test cases. Include accept and reject cases and don't forget edge cases (like empty input)