Design a DFA that accepts language L=x∈(0,1,2): sum of digits in x is 2 mod 3.

Question

how do I make a dfa for this Please guide.

Comments

here what does it mean by sum of digits in x?

where x belongs to {0,1,2}

Answer 1

A good first step for designing automata is to think about what states you will need.

Here, you would need to remember the sum –

which is not possible with a DFA

– but thankfully, we only need to remember the sum in mod3 arithmetic,

which means it can only have three distinct values: 0, 1 or 2…

Therefore, we can keep track of the sum mod 3 with a finite number of states. Then you need to devise the state transitions between the states representing these values.

A convenient fact of modular arithmetic to remember is that a+b≡a−(n−b) mod n ...

 

1. https://www.youtube.com/watch?v=VirRUZ7UuPA