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

Abstract

Computational mechanics quantifies structure in a stochastic process via its causal states, leading to the process's minimal, optimal predictor---the $\epsilon$-machine. We extend computational mechanics to communication channels between two processes, obtaining an analogous optimal model---the $\epsilon$-transducer---of the stochastic mapping between them. Here, we lay the foundation of a structural analysis of communication channels, treating joint processes and processes with input. The result is a principled structural analysis of mechanisms that support information flow between processes. It is the first in a series on the structural information theory of memoryful channels, channel composition, and allied conditional information measures.Comment: 30 pages, 19 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/et1.htm; Updated to conform to published version plus additional corrections and update