## Abstract

Different versions of the notion of almost-periodicity are natural generalizations of the notion of periodicity. The notion of strict almost-periodicity appeared in symbolic dynamics, but later proved to be fruitful in mathematical logic and the theory of algorithms as well. In the paper, a class of essentially almost-periodic sequences (i.e., strictly almost-periodic sequences with an arbitrary prefix added at the beginning) is considered. It is proved that the property of essential almost-periodicity is preserved under finite-automaton transformations, as well as under the action of finite transducers. The class of essentially almost-periodic sequences is contained in the class of almost-periodic sequences. It is proved that this inclusion is strict.

Original language | English (US) |
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Pages (from-to) | 710-714 |

Number of pages | 5 |

Journal | Mathematical Notes |

Volume | 80 |

Issue number | 5-6 |

DOIs | |

State | Published - Nov 2006 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- Finite automaton
- Finite transducer
- Strictly almost-periodic sequence