Deterministic Finite Automata 1. Prove that the following language is regular, either by exhibiting a regular expression representing the language, or a DFA that recognizes the language: (a) (7 points) L={ww does not contain the substring 001 } (b) (3 points) Explain why we can use either a regular expression or a DFA to show that the language L is regular. 2. Consider the DFA M2 shown below. (a) ( 7 points) Give the formal 5-tuple deseription of M2, similar to the example presented in class. (b) (5 points) What is the language of M2 ? 3. In certain programming languages, comments appear between delimiters such as / # and #/. Let C be the language of all valid delimited comment strings. A member of C must begin with /\# and end with \#/ but have no intervening \#/. For simplicity, assume that the alphabet for C is ={a,b,/,#}. (a) ( 7 points) Give a DFA that recognizes C. (b) ( 7 points) Give a regular expression that generates C