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3 Answers

5 votes
5 votes

L={ a^n : n mod 3 = 0} U { a^n : n mod 5 = 1}

Given:

step 1: n mod 3 = 0

put n = 0 ==> 0 mod 3 = 0

==>a^0 = ∈

step 2 : n mod 5 = 1

put n = 2 ==> 2 mod 5 = 1

==>a^2="aa"

L=(a^0) U (a^2) ==>(∈) U ("aa")

so that "aa" is the minimum string accept by the language and the DFA is given below

3 votes
3 votes
N(a) mod 5 =1  OR  N(a) mod 3=0

Shortcut :when divisors are relatively prime then no.of minimum states = 5*3 even operator may be AND.. OR or AND doesn't matter over here...
edited by
2 votes
2 votes

Minimum Number of states in DFA =15

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