Abstract

We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π 0 1 class P is a subshift if and only if there is a computable function F mapping 2 N to 2 N such that P is the set of itineraries of elements of 2 N. Π 0 1 subshifts are constructed in 2 N and in 2 Z which have no computable elements. We also consider the symbolic dynamics of maps on the unit interval. 1