In the box on page 384, a state machine M is given that accepts finite inputs x of the form (1), (1; 0; 1), (1; 0; 1; 0; 1), etc.(a) Write a regular expression that describes these inputs. You may ignore stuttering reactions.(b) Describe the output sequences in La(M ) in words, and give a regular expression for those output sequences. You may again ignore stuttering reactions.(c) Create a state machine that accepts output sequences of the form (1), (1; 0; 1),(1; 0; 1; 0; 1), etc. (see box on page 384). Assume the input x is pure and thatwhenever the input is present, a present output is produced. Give a deterministic solution if there is one, or explain why there is no deterministic solution.What input sequences does your machine accept?