We assume that the input string is put on the TAPE with the symbol # inserted in front of it in cell i.

For example, the input ba will be run with the TAPE initially in the form #baA .... The TM is then

The language this TM accepts is DOUBLEWORD, the set of all words of the form ww where w is a nonnull string in {a,b}*.

DOUBLEWORD = {aa bb aaaa abab baba bbbb aaaaaa aabaab . . }

(i) Explain the meaning of each state and prove that all words in DOUBLEWORD are accepted by this TM.

(ii) Show that all words not in DOUBLEWORD are rejected by this machine.

Please show all the steps. Thanks!

(a A,R) (b.B,R) (a,a,R) (b.b,R) (a,a,R) (b,b,R) (AAR) (A,A,R) (B,B,R) (AAL) (X,X,L) (b,b.L) (a,a,L) (b, Y.L) (a,X,L) (A,A.L) (a,a,L) (b,b,L) (B.BL ((B.B.R C.R (A,A,R) (A,A,R) 9 (BB.R) (B,HR) (#,#,R) 10 (A,AR) 13 (B,B,L) (B,B,L) (A.A.L) (A,A,L) HALT