My question is in response to this answer: http://cs.stackexchange.com/a/18614/22902.
I'm not completely sure about the etiquette about asking questions regarding year-old answers, but I'm assuming I am following protocol by creating a new question. If I am incorrect, please inform me.
My question is: what would the finite automata look like for $L_1$ and $L_0$ in the answer?
- what would the finite automata look like for $L_1$ and $L_0$ in the answer?
I get how the languages are formed; however, since $M_L$ cannot remember how many times it has looped, how does $q$ branch off (if it does) into the two different DFAs for $L_1$$L_0$ and $L_2$$L_1$?
Definitions:
$L$ = infinite regular language
$q$ = state within the DFA for $L$, $M_L$, where $M_L$ loops
$L_1$ = {w in A | $q$ is visited an odd number of times}
$L_0$ = {w in A | $q$ is visited an even number of times}
$L$ = infinite regular language
$q$ = state within the DFA for $L$, $M_L$, where $M_L$ loops
$L_1$ = {w in A | $q$ is visited an odd number of times}
$L_0$ = {w in A | $q$ is visited an even number of times}
Thank you in advance for any help.