@article {IOPORT.02113949,
    author       = {Nishio, Hidenosuke and Saito, Takashi},
    title        = {Information dynamics of cellular automata. I: An algebraic study.},
    year         = {2003},
    journal      = {Fundamenta Informaticae},
    volume       = {58},
    number       = {3-4},
    issn         = {0169-2968},
    pages        = {399-420},
    publisher    = {Polish Mathematical Society, Warsaw; IOS Press, Amsterdam},
    abstract     = {Summary: Information dynamics of Cellular Automata (CA) is studied using polynomials over finite fields. The information about the uncertainty of cell states is expressed by an indeterminate $X$ called information variable and its dynamics is investigated by extending CA to CA[$X$] whose cell states are polynomials in $X$. For the global configuration of extended CA[$X$], new notions of completeness and degeneracy are defined and their dynamical properties are investigated. A theorem is proved that completeness equals non-degeneracy. With respect to the reversibility, we prove that a CA is reversible, if and only if its extension CA[$X$] preserves the set of complete configurations. Information dynamics of finite CAs and linear CAs are treated in separate sections. Decision problems are also referred to.},
    identifier   = {02113949},
}