# Turing Machine for a is smaller than b in theory of automata

Let us begin with Turing Machine for a is less than b, a^{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 the 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.

## Video Lecture with full of Animations

**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.

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