In Definition 0.4, does “for any” mean “there exists two states such that the statement holds”, or “for all pairs of states, the statement holds”?
It means that for all pairs of distinct states, their associated environments (sets of compatible observation sequences) are disjoint.
Oops. I didn’t look at the notation closely and assumed a substantially different thing based on the word “distinguishable”. Oh well, I hope you guys will think my application was adequate anyway.
Thanks!
In Definition 0.4, does “for any” mean “there exists two states such that the statement holds”, or “for all pairs of states, the statement holds”?
It means that for all pairs of distinct states, their associated environments (sets of compatible observation sequences) are disjoint.
Oops. I didn’t look at the notation closely and assumed a substantially different thing based on the word “distinguishable”. Oh well, I hope you guys will think my application was adequate anyway.
Thanks!