title: NP-completeness conditions for some types of systems of linear diophantine comparisons and equations consistency checking
metadata.name: dc.contributor.author
metadata.value: Kosovskii, Nikolay K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kosovskaya, Tatiana M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Kosovskii, Nikolay N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-08-01T10:34:54Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-08-01T10:34:54Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-06
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/2455
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Three series of number-theoretic problems concerning systems of modulo m comparisons and systems
  of Diophantine linear 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 m1 and m2 (m1 < m2 and m1 is not a divisor of m2) the consistency
  problem for a system of simultaneously modulo m1 and m2 comparisons every of which contains exactly
  3 variables is NP-complete.
  It is also proved that for every m >2 the consistency on the subset containing at least two elements
  of the set {0, . . .,m − 1} problem for a system of modulo m comparisons every of which contains exactly
  3 variables is NP-complete. If P =NP then the statement of the proved theorem can not be changed by
  means of replacing the term «3-comparison» with the term «2-comparison».
  For a system of Diophantine linear equations every of which contains exactly 3 variables it is proved
  the NP-completeness of the problem of its consistency on the interval of integers. If P =NP then the statement
  of the proved theorem can not be changed by means of replacing the term «3-equation» with the term
  «2-equation». This problem also admits a simple geometrical interpretation concerning NP-completeness
  of the checking whether there exists inside a many-dimensional cube an integer-valued point of intersection
  of hyperplanes which cut off equal segments of three axes and are parallel to the other ones.
  Among the problems of the series there are practically useful problems. If P =NP then, as the set
  of all values for a variable of a computer type integer may be considered as the set of integer values from
  a segment then theorem proves that there does not exist a polynomial algorithm solving such a system in
  the set of all numbers of the type integer. Refs 6.
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;Vol. 3 (61); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: system of linear Diophantine equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: system of linear Diophantine comparisons
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 comparisons and equations consistency checking
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Косовский_Косовская_Косовский.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/2455/1/%d0%9a%d0%be%d1%81%d0%be%d0%b2%d1%81%d0%ba%d0%b8%d0%b9_%d0%9a%d0%be%d1%81%d0%be%d0%b2%d1%81%d0%ba%d0%b0%d1%8f_%d0%9a%d0%be%d1%81%d0%be%d0%b2%d1%81%d0%ba%d0%b8%d0%b9.pdf
resources.format: Adobe PDF
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