Number of states in a minimal DFA construction

Question

Suppose L is a regular language of all a's and b's where the number of a's is divisible by m and the number of b's is divisible by n. If M is the minimal DFA accepting language L, then what is the number of states in M ? Is it nm or (n+1)(m+1) ?

Comments

It is n*m

Answer 1

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Comments

In such questions where we the number of states in minimal DFA are asked, do we have to count the trap state also?

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yes we will count the trap state also it is not NFA it DFA for invalid string there will be a trap state if u remove that ur ans will be wrong

Answer 2

Finite automata is capable of performing modular counting. By saying mod2 it means it has seen 2 inputs for the same. Similarly for xmodn, means n states required.   So, n*m.

Comments

X mod n means n states are required.

So, n*m. What is m? Please explain.