Computational Mechanics of Input-Output Processes: Structured transformations and the $\epsilon$-transducer

摘要

Computational mechanics quantifies structure in a stochastic process via itscausal states, leading to the process's minimal, optimal predictor---the$\epsilon$-machine. We extend computational mechanics to communication channelsbetween two processes, obtaining an analogous optimal model---the$\epsilon$-transducer---of the stochastic mapping between them. Here, we laythe foundation of a structural analysis of communication channels, treatingjoint processes and processes with input. The result is a principled structuralanalysis of mechanisms that support information flow between processes. It isthe first in a series on the structural information theory of memoryfulchannels, channel composition, and allied conditional information measures.