Effective Symbolic Dynamics

Authors:
Douglas Cenzer;S. Ali Dashti;Jonathan L. F. King
Affiliations:
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA;Department of Mathematics, University of Florida;Department of Mathematics, University of Florida
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

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Abstract

We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable @P"1^0 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. A @P"1^0 subshift is constructed which has no computable element. We also consider the symbolic dynamics of maps on the unit interval.