I do not understand how to do 2,3, and 4. Please teach me how to do these.

Thank you!

1. (10 points) Consider the FA M1 given below: a,b 90 92 b a. Write a formal definition of Mi. b. Consider strings bab, abaa, abab, E. Which ones are accepted by M? Show the traces of strings in L(M). C. Explain, i.e., describe, what is the language recognized by M. 2. (15 points) Build a deterministic FA M2 for the following language L2 = {x over {a, b} x consists of sequences of two identical symbols). For example, aab L2 and ab L2, but bb L2 and bbaaaabb e L2. 3. (15 points) Build a deterministic FA M3 such that L(M3) = {w over {a,b}||w| 21, length of w is even, and w ends on b}. 4. (15 points) Build a deterministic FA Ma for the following language 4 = {x over {a, b} if x contains sequences of a's then all of them must have odd length} For example, aa L2 and babbaaaa L, but be La E Laba E L and bbaaab e L4. (Hint: in constructing each deterministic FA for problems 2, 3, and 4 make sure to consider all the possibilities, i.e., the different types of strings in the language of the corresponding FA.)