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DOI: 10.4230/LIPIcs.STACS.2022.37
URN: urn:nbn:de:0030-drops-158474
URL: https://drops.dagstuhl.de/opus/volltexte/2022/15847/
Idziak, Paweł M. ; Kawałek, Piotr ; Krzaczkowski, Jacek
Satisfiability of Circuits and Equations over Finite Malcev Algebras
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Abstract
We show that the satisfiability of circuits over finite Malcev algebra A is NP-complete or A is nilpotent. This strengthens the result from our earlier paper [Idziak and Krzaczkowski, 2018] where nilpotency has been enforced, however with the use of a stronger assumption that no homomorphic image of A has NP-complete circuits satisfiability. Our methods are moreover strong enough to extend our result of [Idziak et al., 2021] from groups to Malcev algebras. Namely we show that tractability of checking if an equation over such an algebra A has a solution enforces its nice structure: A must have a nilpotent congruence ν such that also the quotient algebra A/ν is nilpotent. Otherwise, if A has no such congruence ν then the Exponential Time Hypothesis yields a quasipolynomial lower bound. Both our results contain important steps towards a full characterization of finite algebras with tractable circuit satisfiability as well as equation satisfiability.
BibTeX - Entry
@InProceedings{idziak_et_al:LIPIcs.STACS.2022.37,
author = {Idziak, Pawe{\l} M. and Kawa{\l}ek, Piotr and Krzaczkowski, Jacek},
title = {{Satisfiability of Circuits and Equations over Finite Malcev Algebras}},
booktitle = {39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
pages = {37:1--37:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-222-8},
ISSN = {1868-8969},
year = {2022},
volume = {219},
editor = {Berenbrink, Petra and Monmege, Benjamin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/15847},
URN = {urn:nbn:de:0030-drops-158474},
doi = {10.4230/LIPIcs.STACS.2022.37},
annote = {Keywords: Circuit satisfiability, solving equations, Exponential Time Hypothesis}
}
| Keywords: | Circuit satisfiability, solving equations, Exponential Time Hypothesis | |
| Seminar: | 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 09.03.2022 |
