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DC Field | Value | Language |
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dc.contributor.author | Kosovskii, Nikolai K. | - |

dc.contributor.author | Kosovskaya, Tatiana M. | - |

dc.contributor.author | Kosovskii, Nikolai N. | - |

dc.date.accessioned | 2016-09-28T15:51:00Z | - |

dc.date.available | 2016-09-28T15:51:00Z | - |

dc.date.issued | 2016-09 | - |

dc.identifier.citation | Kosovskii N.K., Kosovskaya T.M., Kosovskii N.N. NP-completeness conditions for some types of systems of linear diophantine dis-equations consistency checking. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 3, pp. 408–414. | en_GB |

dc.identifier.other | 10.21638/11701/spbu01.2016.308 | - |

dc.identifier.uri | http://hdl.handle.net/11701/3910 | - |

dc.description.abstract | Three series of number-theoretic problems concerning systems of Diophantine linear dis-equations with explicitly pointed out parameters are proposed in this part of the paper. Conditions upon the parameters implying that every problem of a series is an NP-complete one are proved. It is proved that for every m and m (m < m ) the consistency problem for a system of Diophantine linear dis-equations every of which contains exactly 3 variables (even if every coefficient belongs to {−1, 1}) is NP-complete. This problem also admits a simple geometrical interpretation concerning NP-completeness of the checking whether inside a many-dimensional cube there exists an integer-valued point which does not belong to any of the given hyperplanes which cut off equal segments of three axes and are parallel to the other ones. If every dis-equation of a system of Diophantine linear dis-equations contains exactly 2 variables then the problem remains an NP-complete one under the condition that m −m > 2. It is also proved that if a solution of a system of Diophantine linear dis-equations every of which contains exactly 3 variables must belong to a domain, which is defined by a system of polynomial inequalities, contains an n-dimentional cube and is contained in an n-dimentional parallelogramm, then it is an NP-complete one. Refs 15. | en_GB |

dc.language.iso | ru | en_GB |

dc.publisher | St Petersburg State University | en_GB |

dc.relation.ispartofseries | Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Issue 3 | - |

dc.subject | system of linear Diophantine dis-equations | en_GB |

dc.subject | belonging of a integer-valued point from a bounded domain to the intersection of hyperplanes | en_GB |

dc.subject | NP-completeness | en_GB |

dc.title | NP-completeness conditions for some types of systems of linear diophantine dis-equations consistency checking | en_GB |

dc.type | Article | en_GB |

Appears in Collections: | Issue 3 |

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Kosovskiy.pdf | 217,08 kB | Adobe PDF | View/Open |

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