Extend the framework beyond stationarity and discrete alphabets

Extend the theoretical framework and results to non-stationary stochastic processes and to general (potentially continuous) alphabets by removing the current assumptions that the time series Xt is stationary and takes values on a discrete alphabet, and establish the corresponding definitions and theorems for these broader settings.

Background

In the Appendix, the authors specify that their formal development assumes discrete alphabets and stationarity to simplify results. They note that while extensions are possible, they are not provided in the current work.

Relaxing these assumptions would broaden applicability to many real-world systems that are non-stationary or involve continuous-valued variables, requiring careful reformulation of the core constructs (e.g., causal states, e- and v-machines) and proofs.