On the Fragmentary Complexity of Symbolic Sequences

A measure of the ability of a symbolic sequence to be coded by initial fragments of another symbolic sequence is introduced and its basic properties are investigated. Applications to the characterization of symbolic sequences associated with shift mappings on a torus corresponding to a special partitioning of the torus and to multi-rate systems of coprocessors are considered. P. Diamond, P. Kloeden and A. Pokrovskii were supported by the Australian Research Council Grant A 8913 2609, V.Kozyakin was partially supported by the Russian Foundation for Fundamental Research Grant 93012884. Department of Mathematics, University of Queensland, Brisbane, Qld 4072, Australia School of Computing and Mathematics, Deakin University, Geelong, Victoria 3217, Australia Institute of Information Transmission Problems, Russian Academy of Sciences, 19 Ermolovoy str., Moscow 101447, Russia