An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
On topological dynamics of Turing machines
Theoretical Computer Science
Theoretical Computer Science
On the presence of periodic configurations in Turing machines and in counter machines
Theoretical Computer Science
Dynamics of a class of ants on a one-dimensional lattice
Theoretical Computer Science - Discrete applied problems, florilegium for E. Goles
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
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We consider the Turing Machine as a dynamical system and we study a particular partition projection of it. In this way, we define a language (a subshift) associated to each machine. The classical definition of Turing Machines over a one-dimensional tape is generalized to allow for a tape in the form of a Cayley Graph. We study the complexity of the language of a machine in terms of realtime recognition by putting it in relation with the structure of its tape. In this way, we find a large set of realtime subshifts some of which are proved not to be deterministic in realtime. Sofic subshifts of this class correspond to machines that cannot make arbitrarily large tours. We prove that these machines always have an ultimately periodic behavior when starting with a periodic initial configuration, and this result is proved for any Cayley Graph.