Geodesic
Almost periodicity, finite automata mappings, and related effectiveness issues
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2010), pp. 74-87

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We introduce a class of eventually almost periodic sequences where some suffix is almost periodic (i.e., uniformly recurrent). The class of generalized almost periodic sequences includes the class of eventually almost periodic sequences, and we prove this inclusion to be strict. We also prove that the class of eventually almost periodic sequences is closed under finite automata mappings and finite transductions. Moreover, we obtain an effective form of this result. In conclusion we consider some algorithmic questions related to the almost periodicity.
Keywords: almost periodic sequences, finite automata, effectiveness. 
@article{IVM_2010_1_a7,
     author = {Yu. L. Pritykin},
     title = {Almost periodicity, finite automata mappings, and related effectiveness issues},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {74--87},
     publisher = {mathdoc},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_1_a7/}
}
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Yu. L. Pritykin. Almost periodicity, finite automata mappings, and related effectiveness issues. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2010), pp. 74-87. http://geodesic.mathdoc.fr/item/IVM_2010_1_a7/