GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 24

Answer 1

Detailed Video Solution: https://www.youtube.com/watch?v=kPLciwgwKaE

Comments

As DFA, we should have all transitions for every state on every input {a,b,c} (keep an eye on the size of the input)

so we should leave out the last state as the required is finite language (refer deepak sir's video: https://www.youtube.com/watch?v=kPLciwgwKaE) 



Maximum number of strings we can accept is given as 

$= 3^{0} +3^{1} +3^{2} +3^{3} +3^{4} +3^{5} +3^{6} $

$= \frac{3^{6+1}  – 1 }{ 3 – 1 }$

$= \frac{ 2187  – 1 }{ 3 – 1 }$

$= \frac{ 2186 }{ 2}$

$= 1093 $