**Turing Machine for a is less than b, a**^{m}b^{n} where a=b or m=n

^{m}b

^{n}where a=b or m=n

**Logic:**

If machine reads anyone a from the input tape, then machine write X and if machine reads any b then machine write y;

a = X

b = Y

in the end, the machine must read Y, write Y and move right as illustrated in diagram(start to state 4).

After that, there are multiple b’s to enforce that b’s are larger in number and a’s are smaller in number.

**Accepted strings:**

Such kind of strings should be accepted by Turing Machine.

e.g, abB, aabbbb, aaabbbbb,…..etc.

**Rejected strings:**

Such kind of strings should be rejected by Turing Machine.

e.g, ab, aab, aaabb,…..etc.