Herrmann, Christian (2024)
On the complexity of equational decision problems for finite height complemented and orthocomplemented modular lattices.
In: Algebra universalis, 2022, 83 (1)
doi: 10.26083/tuprints-00023423
Article, Secondary publication, Publisher's Version
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Item Type: | Article |
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Type of entry: | Secondary publication |
Title: | On the complexity of equational decision problems for finite height complemented and orthocomplemented modular lattices |
Language: | English |
Date: | 3 September 2024 |
Place of Publication: | Darmstadt |
Year of primary publication: | 31 December 2022 |
Place of primary publication: | Basel |
Publisher: | Springer International Publishing |
Journal or Publication Title: | Algebra universalis |
Volume of the journal: | 83 |
Issue Number: | 1 |
Collation: | 28 Seiten |
DOI: | 10.26083/tuprints-00023423 |
Corresponding Links: | |
Origin: | Secondary publication DeepGreen |
Abstract: | We study the computational complexity of the satisfiability problem and the complement of the equivalence problem for complemented (orthocomplemented) modular lattices L and classes thereof. Concerning a simple L of finite height, NP-hardness is shown for both problems. Moreover, both problems are shown to be polynomial-time equivalent to the same feasibility problem over the division ring D whenever L is the subspace lattice of a D-vector space of finite dimension at least 3. Considering the class of all finite dimensional Hilbert spaces, the equivalence problem for the class of subspace ortholattices is shown to be polynomial-time equivalent to that for the class of endomorphism ∗-rings with pseudo-inversion; moreover, we derive completeness for the complement of the Boolean part of the nondeterministic Blum-Shub-Smale model of real computation without constants. This result extends to the additive category of finite dimensional Hilbert spaces, enriched by adjunction and pseudo-inversion. |
Uncontrolled Keywords: | Ortholattice of subspaces, Matrix*-ring, Complemented modular lattice, Satisfiability problems, Complexity, Hilbert category |
Identification Number: | Artikel-ID: 5 |
Status: | Publisher's Version |
URN: | urn:nbn:de:tuda-tuprints-234239 |
Classification DDC: | 500 Science and mathematics > 510 Mathematics |
Divisions: | 04 Department of Mathematics > Logic |
Date Deposited: | 03 Sep 2024 13:39 |
Last Modified: | 03 Sep 2024 13:39 |
SWORD Depositor: | Deep Green |
URI: | https://tuprints.ulb.tu-darmstadt.de/id/eprint/23423 |
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