Just want to make sure that the way I solved this question is correct since I looked around online and am still not sure about this part: Question: draw a finite state machine that generates $\{0^∗(10+11)^∗\}$
From what I understood in the powerpoint:
step 1 : 1 state per symbol, so $s_0, s_1$
step 2 : 1 additional state as finishing state, $s_f$
Rules for producting the expresssion:
if $A \rightarrow aB$ there is a transition between $s_A$ and $s_b$
if $A \rightarrow a$, $s_A$ is an accept state
$$S \rightarrow \epsilon$$ $$S \rightarrow AB$$ $$A \rightarrow 0A, \space \epsilon$$
At this point I'm not sure how to write the production rules anymore ... if I understood correctly $(10+11)^∗$ means all combinations of 10, 11, 1011 and 1101 so it can be written as $ 1 (1 \cup 0)$.
Intuitively I understand that $s_0$ is a accept state and loops back on itself, then transitions into $s_1$ which is not an accept state, then transitions into an accept state $s_f$ when either 1 or 0 is read which can then transfer back to $s_1$ when an 1 is read.
Here's an attempt I made: $$B \rightarrow 1B$$ $$B \rightarrow 0B$$ $$B \rightarrow 0$$ $$B \rightarrow 1$$
however this would allow for strings such as 1001 which is not allowed. I've also tried
$$B \rightarrow 10B$$ $$B \rightarrow 11B$$ $$B \rightarrow \epsilon$$
But I'm not sure how this translate to a state machine.
Thanks