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dc.contributor.authorKosovskii, Nikolai K.-
dc.contributor.authorKosovskaya, Tatiana M.-
dc.contributor.authorKosovskii, Nikolai N.-
dc.date.accessioned2016-09-28T15:51:00Z-
dc.date.available2016-09-28T15:51:00Z-
dc.date.issued2016-09-
dc.identifier.citationKosovskii 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.other10.21638/11701/spbu01.2016.308-
dc.identifier.urihttp://hdl.handle.net/11701/3910-
dc.description.abstractThree 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.isoruen_GB
dc.publisherSt Petersburg State Universityen_GB
dc.relation.ispartofseriesVestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Issue 3-
dc.subjectsystem of linear Diophantine dis-equationsen_GB
dc.subjectbelonging of a integer-valued point from a bounded domain to the intersection of hyperplanesen_GB
dc.subjectNP-completenessen_GB
dc.titleNP-completeness conditions for some types of systems of linear diophantine dis-equations consistency checkingen_GB
dc.typeArticleen_GB
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