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Let Σ = {0, 1, 2}. Draw the diagram of a finite state machine that takes...

Let Σ = {0, 1, 2}. Draw the diagram of a finite state machine that takes as input two strings from Σ∗ and outputs their sum (as ternary strings). The machine should read pairs of digits at a time – one from the first string in the sum, and one from the second string in the sum.

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As, when a number is divided by 3, there are only 3 possibilities. The remainder can be either 0, 1 or 2. Here, state 0 represents that the remainder when the number is divided by 3 is 0. State 1 represents that the remainder when the number is divided by 3 is 1 and similarly state 2 represents that the remainder when the number is divided by 3 is 2. So if a string reaches state 0 in the end, it is accepted otherwise rejected.

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