The Hartley function, the main measure of Nonspecificity, is essentially based on the count of all possible states. However, while coding the Hartley, I realized that "possible" means all remaining state descriptions, regardless of whether they are reachable or not from all other states. Let me give an intuitive example of a situation where this might make a difference: ages ago my best friend and I got carried away playing the video game Gauntlet till 9 am and on occasion, we noticed that the maze generator would sometimes create an open cell that was completely walled in; sometimes the game would generate a monster within that would be permanently stuck there, for the lifetime of that maze. In some situations, it may be helpful to disqualify such unreachable states when quantifying information.
Are there variants of the Hartley function or other Nonspecificity measures that address this? Perhaps there's something in the field of Markov chains, which I'm even less familiar with? Then again, perhaps it would be difficult to determine the reachability of all states in advance without running into Traveling Salesmen-type problems. Moreover, it begs the question of which group of states takes precedence - is Group A reachable from B and C, or are B and C reachable from A? I suppose that means that we could derive separate Nonspecificity figures for each subgroup, which incidentally probably wouldn't obey the triangle inequality or exhibit symmetry. The Hartley Function would essentially act as an upper bound against any such measure. This is not a pressing problem at this moment; I'm just trying to do a thorough job of coding as many alternative information measures as I can, little by little in order to familiarize myself with the field, and see a niche here that I haven't seen filled yet. Of course, I'm an amateur whose still unfamiliar with these topics, so if such a measure exists I'd probably be ignorant of it. Thanks in advance for any input. :)