construct a DFA to check if a string containing a,b and no.of a's is divisible by...

construct a DFA to check if a string containing a,b and no.of a's is divisible by 5 and no.of b's is divisible by 7

Expert Solution

So basically to design a DFA, we first need to decide what will be the states.

Here, I've chosen states q_ij which denotes a state where ( number of a's ) % 5 = i and ( number of b's ) % 7= j

So basically we move from one state to another according to the character being considered.

The logic for moving from q_i6 to q_i0 when b is encountered is simple as, that if a number mod 7 is 6 that means adding 1 more, will make it divisible by 7 and resulting in 0 as remainder.

Similar is the reason for q_6j to q_0j when an a is encountered.

q₀₀ is the finalstate as only there, the number of a's are divisible by 5 and number of b's are divisible by 7.

Another than that, it is a normal DFA and all conditions are understandable.

venereology answered 2 years ago

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