Question

Let L = {0^n 1^n | n ≥ 0}. Draw the state diagram of a Turing machine deciding L= Σ∗\L(basically the complement of L), where Σ = {0,1}, and Γ = {0,1,#,U}, and “\” is set subtraction.

Let L = {0"1" | n > 0}. Draw the state diagram of a Turing machine deciding I = * \ L (basically the complement of L), where = {0,1), and I = {0,1,#,0}, and "" is set subtraction.

I understand that the complement of L will be {0^n 1^m | n=!m} U {(0 U 1)* 1 0 {0 U 1)*}.

How should I draw the state diagram with this?

Answer 1

1/1,R of is blank. olo, R. 710, olo, R 30,R To,R 110,L olo, 1/1, L {09;" | n20} A-B-E-C: Matching o's with 1's If there's not a 1 at end for ook If it isn't starting with a o, accepting.

• Transitions from A-F and E-F make all the difference. Rest looks similar but not same if you can see through.

• A-F and E-F are for mismatches and rest of the turing machine is for a^nb^n. A-F is for 1 before 0 or without 0. E-F is for 0 for 0 instead of 1. Those two are valid cases for complement condition.

Let me know if you still have any doubts.