if you know how to answer these question and know theoritical computer science. write your email clearly and i will contact you

1.27 Read the informal definition of the finite state transducer given in Exercise 1.24. Give the state diagram of an FST with the following behavior. Its input and output alphabets are {0,1). Its output string is identical to the input string on the even positions but inverted on the odd positions. For example, on input 0000111 it should output 1010010. 1.28 Convert the following regular expressions to NFAs using the procedure given in Theorem 1.54. In all parts, = {a, b}. a. a(abb) Ub b. at u (ab)* c. (a Uba*b* 1.29 Use the pumping lemma to show that the following languages are not regular. Aa. Az = {0"1" 2"| n >0} b. A2 = {www w {a, b}"} Ac. Az = {a?"| n >0} (Here, a?" means a string of 2" a's.) I 1.30 Describe the error in the following "proof that 0*1* is not a regular language. (An error must exist because 0*1' is regular.) The proof is hy contradiction. Assume that 0*1' is regular. Let p be the pumping length for 0*1* given by the pumping lemma. Choose 8 to be the string OP1P. You know that s is a member of o*1', but Example 1.73 shows that s cannot be pumped. Thus you have a contradiction. So 0 1 is not regular