Finite-state automation that accepts sum of digits divisible by n

Question

Finite state machine that accepts if sum of digits divisible by 3 .

I am trying to construct a finite state machine the accepts if the sum of digits is divisible by n. So far I was able to do for n=2 and n=3 but dint find any generalized steps that I could follow. Any help is appreciated.

Can you show how you handled the cases for n=2, 3? – pgpb.padilla Nov 29 '15 at 05:56 — pgpb.padilla, Nov 29 '15 at 05:56
@ pgpb.padilla I have added an image for n=3. – user5616894 Nov 29 '15 at 07:32 — user5616894, Nov 29 '15 at 07:32

score 0 · Answer 1 · answered Nov 29 '15 at 05:56

This question is a little vague but it seems like you are trying to accept a stream of numbers if they are divisible by n.

If this is the case I would suggest you gathering input, separating by digit, summing the digits and using a mod. Some clarification would help my answer though.

score 0 · Answer 2 · answered Dec 22 '15 at 08:56

It seems like your alphabet is ternary and that it consists of 0, 1, and 2. For any n, you must have an n-state machine with each state representing the remainder when dividing by n. The transition for any x equal to 0, 1, or 2 from state z will go to state (z+x)%n where "%" represents the remainder operator.

Finite-state automation that accepts sum of digits divisible by n

2 Answers2