Geodesic
On the complexity of recurring sequences
Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 52-62
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We study recurring sequences over finite fields sets and the set $\mathbf N=\{0,1,2,\ldots\}$. The complexity of recurring sequences over finite sets is estimated as the complexity of computing on determinate linearly bounded automata. We introduce the notion of a branching recurring sequence. The complexity of branching recurring sequences over finite sets is estimated as the complexity of computing on non-determinate linearly bounded automata. Recurring sequences over the set $\mathbf N$ simulate computations on multi-tape Minsky machines. We ascertain undecidability of some problems concerning this type of recurring sequences. This research was supported by the Russian Foundation for Basic Research, grant 00–01–00351. 
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S. S. Marchenkov. On the complexity of recurring sequences. Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 52-62. http://geodesic.mathdoc.fr/item/DM_2003_15_2_a3/

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