>Any computer program (without network stuff or inputs for a time (assume your computer has a true RNG module)) you could run is a Markov process. Just say that your state space is the space of possible ways the memory of the computer can be.

No. The entire computer is a Markov process in that situation. An individual process may still remember its past states and therefore not be Markovian. See the example I gave about allowing or blocking transactions.

By “memory” I was including whatever is on disk, and the values of all the CPU registers, and all the CPU flags, etc.

So, yeah, the state of the computer (regarded as an abstract machine, not viewed at the level of the physical hardware)

Oh, you mean because I said a particular program, and other things on the computer could interfere with the program. Ok, point. I was imagining a computer that just had a single program running on it (with no separate OS) I guess? But yeah, good point, I certainly didn’t make my idea precise enough (in my own mind or in my words).

Yes, I understood what you meant and my answer assumes that the contents of all memory -- volatile and persistent -- constitute the state of the machine.

It doesn't matter whether the program is the only thing the computer is doing or whether there are other things running on the same machine. The program considered as a machine unto itself is a conceptually different thing from the underlying hardware. The Markov property is a way to reason about how a process interacts with its state. "I could design a Markov process that's semantically equivalent to a non-Markov process, by just including more state" is a pointless statement. The whole point of the discrimination is to reason about the thing you're studying.