Please explain in details. DFA

1. Construct a DFA to accept a language consisting of the set of all strings that do not contain three consecutive a s. Note that ={a,b} 4 points 2. Construct a DFA to accept a language consisting of the set of all strings that have exactly two occurrences of a. Note that ={a,b} 4 points 3. Construct a DFA that accepts the language L={w:Na(w)mod3=1}, where Na(w)=No. of a s i string w. Note that ={a,b} 4 points 4. We say that a DFA M for a language A is minimal if there does not exist another DFA Mx for A such that Mx has strictly fewer states than M. Suppose that M=(Q,,,q0,F) is a minimal DFA for A. Usir M, we construct a DFA M for the complement AAsM=(Q,,,q0,QF). Prove that Mis a minima DFA for A. 2 points 5. Construct NFAs with the specified number of states for each of the following languages, where ={0,1} a. {w:w ends with 00} in three states. 2 points b. {w : w contains the substring 0101} with five states. 2 points c. {w : w contains an even number of 0 's or exactly two 1 s } with six states. 2 points