摘要

In this note, we presents some discussions on symbolic representations of dynamical systems through shifts and subshifts. By employing the tool of symbolic dynamics, we show that there exists a conjugate representation between general symbolic dynamical systems and usual symbolic dynamical systems through subshifts. For any one-dimensional cellular automaton, we demonstrate that there exists a subsystem such that it is a semi-conjugate representation of the cellular automaton through the shift.