Deciding whether a Lattice has an Orthonormal Basis is in co-NP

Deciding whether a Lattice has an Orthonormal Basis is in co-NP

We show that the problem of deciding whether a given Euclidean lattice L has an orthonormal basis is in NP and co-NP. Since this is equivalent to saying that L is isomorphic to the standard integer lattice, this problem is a special form of the Lattice Isomorphism Problem, which is known to be in th...

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1. Verfasser: Hunkenschröder, Christoph
Format: Artikel
Sprache:eng
Schlagworte:
Computer Science - Discrete Mathematics
Mathematics - Combinatorics
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Zusammenfassung:We show that the problem of deciding whether a given Euclidean lattice L has an orthonormal basis is in NP and co-NP. Since this is equivalent to saying that L is isomorphic to the standard integer lattice, this problem is a special form of the Lattice Isomorphism Problem, which is known to be in the complexity class SZK.
DOI:10.48550/arxiv.1910.03838