This is another homework problem I'm stuck with. For the given finite automata, I am asked to find out the equivalent regular expression.
On inspecting the given automata, I started deducing the expressions that it accepts and tried to find a pattern, and this is what I was able to figure out -
The automata makes the following transitions to a final state upon said input -
- $q_1 to \ q_3$ on input of a single symbol $b$, $a^*b$, $ba^*$, or $a^*ba^*$.
- Traversing through the cycle $q_1,q_3,q_2$ (and so on repeating) on input of $(a^*b^4a^*)^*$, a $((a^*b)^4)^*$.
Now the equivalent regular expression must be the sum of all these expressions,
R = $b + (a^*b) + (ba^*) + (a^*ba^*) + (a^*b^4a^*)^* + ((a^*b)^4)^*$.
Is there a better, concise expression for this or am I missing something? If not, How do I approach the simplification process of this expression?