title: NP-completeness conditions for some types of systems of linear diophantine dis-equations consistency checking
metadata.name: dc.contributor.author
metadata.value: Kosovskii, Nikolai K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kosovskaya, Tatiana M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kosovskii, Nikolai N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-09-28T15:51:00Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-09-28T15:51:00Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.308
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/3910
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: system of linear Diophantine dis-equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: belonging of a integer-valued point from a bounded domain to the intersection of hyperplanes
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: NP-completeness
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: NP-completeness conditions for some types of systems of linear diophantine dis-equations consistency checking
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Kosovskiy.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/3910/1/Kosovskiy.pdf
resources.format: Adobe PDF
resources.size: 217,08 kB