Computable symbolic dynamics | Zendy

Cenzer Douglas | Zendy; Dashti S. Ali | Zendy; King Jonathan L. F. | Zendy

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Computable symbolic dynamics

Author(s) -

Cenzer Douglas,

Dashti S. Ali,

King Jonathan L. F.

Publication year - 2008

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200710066

Subject(s) - decidability , computable function , symbolic dynamics , unit interval , mathematics , class (philosophy) , interval (graph theory) , set (abstract data type) , function (biology) , discrete mathematics , pure mathematics , combinatorics , computer science , artificial intelligence , programming language , evolutionary biology , biology

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 exists 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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