### Abstract

A discrete time series over a field F, With π state sets and m time steps, can be described by a function f = (f_{1},...,f_{n}): F^{n} →F^{n}, When F Is a finite field, it is well known that each coordinate function f_{i} is a polynomial in π variables over F. Thus a discrete time series over F can be modeled by a set of polynomials over F. This paper studies the commutative algebra methods to construct a desired polynomial model. Applications of Gröbner Bases techniques in the modeling process were discussed.

Original language | English |
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Title of host publication | Proceedings of Dynamic Systems and Applications - 4th International Conference on Dynamic Systems and Applications |

Editors | G.S. Ladde, N.G. Medhin, M. Sambandham |

Pages | 68-73 |

Number of pages | 6 |

State | Published - 1 Dec 2003 |

Event | Proceedings of the 4th International Conference on Dynamic Systems and Applications - Atlanta, GA, United States Duration: 21 May 2003 → 24 May 2003 |

### Publication series

Name | Proceedings of Dynamic Systems and Applications |
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### Other

Other | Proceedings of the 4th International Conference on Dynamic Systems and Applications |
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Country | United States |

City | Atlanta, GA |

Period | 21/05/03 → 24/05/03 |

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## Cite this

Li, A. (2003). Polynomial models of discrete time series over finite fields. In G. S. Ladde, N. G. Medhin, & M. Sambandham (Eds.),

*Proceedings of Dynamic Systems and Applications - 4th International Conference on Dynamic Systems and Applications*(pp. 68-73). (Proceedings of Dynamic Systems and Applications).