I have been trying to figure out the Arden's Rule and the equational method to transform DFA's & NFA's to RE. I know what the rule state:
if x = s + xr
then x = sr*, with $s,r\in$ Regular Expressions
With that said, when I'm trying to transform one DFA in a RE this questions pop:
For example regarding this DFA
The $\epsilon$ is added in the entry stage A or in the final stage D and A ?
The equations should be written regarding the transitions in or out of a given state
2.1 For example A = $\epsilon$ + 0B + 1C or A = $\epsilon$ + 0C
Can the equational method and Arden's Rule be applied to a NFA with multiple initial states ?
Final thoughts, I have been trying out and it seems that when we count the transitions out of a state the $\epsilon$ should be added to the final state. When we count the transitions into a state the $\epsilon$ should be added to the initial state.
Keep in mind that I SERIOUSLY doubt my conclusions and I really need some help.