Very cool to see an article that discusses Crutchfield's Epsilon machine formalism. It's one of those rare theories that is conceptually powerful but also simple and concrete enough that it can be implemented in a couple hundred lines of code.

For those interested, [1] is a readable (if quirky) introduction to the theory. The paper discussed in this article seems to discuss a way of "stacking" epsilon machines, so that you have a machine that describes the state transitions of a machine that describes a data set. I wonder if this gets around the main weakness of the e-machine formalism, namely that for a process with non-finite memory, there's no obvious next class of automata to try after finite state machines. In a sense FSMs are the only non-arbitrary model of computation; everything else basically boils down to augmenting a finite-state control with a gadget for storing data, like a stack (pushdown automata), register (counter/register machines), random-access tape (Turing machines), random-access tape but you're only allowed a tape the size of the input (linear-bounded automata) etc. You can constrain that gadget in pretty much arbitrary ways, which makes it difficult to choose a computational model for a non-finite process.

[1]: https://csc.ucdavis.edu/~cmg/papers/CalcEmerg.pdf