Sibling comment is very helpful in terms of what linear is. In terms of the abstract, your system isn't "observable" as even with all the inputs and outputs in

Sibling comment is very helpful in terms of what linear is. In terms of the abstract, your system isn't "observable" as even with all the inputs and outputs in a given time period, and knowledge of the hash functions, you still won't be able to work out the internal state. If you had all the inputs since it started you could (assuming it was deterministic and so on) but thats "less observable" in some sense as you need potentially unbounded information. While linear systems are tractable, some nonlinear systems could be tractable too. Software is interesting from this point of view as while its clearly nonlinear, we can create mechanisms to expose otherwise hidden internal state and to control it, although there is generally such a large number of internal states that this is difficult.