I am trying to find the name of the automaton with a beautiful property. No matter which state that you start from, there is a same sequence of $k$ transitions so that you end up reaching at the same state.
Can someone help me find that special type of automaton. Thanks in advance
I believe I was wrong in framing the question. However I found the source I was looking for. So I thought that I would share it.
It appears that every DFA has that property and one can read more about from wiki if you look for "reset sequence" or "synchronizing word".
This video also sheds some light on the same topic. https://www.youtube.com/watch?v=4gsp3CZUtV0
Thanks to HallaSurvivor for looking at the question and making few modifications.