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DOI: 10.4230/LIPIcs.STACS.2021.58
URN: urn:nbn:de:0030-drops-137038
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13703/
Schweitzer, Pascal ; Seebach, Constantin
Resolution with Symmetry Rule Applied to Linear Equations
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Abstract
This paper considers the length of resolution proofs when using Krishnamurthy’s classic symmetry rules. We show that inconsistent linear equation systems of bounded width over a fixed finite field 𝔽_p with p a prime have, in their standard encoding as CNFs, polynomial length resolutions when using the local symmetry rule (SRC-II).As a consequence it follows that the multipede instances for the graph isomorphism problem encoded as CNF formula have polynomial length resolution proofs. This contrasts exponential lower bounds for individualization-refinement algorithms on these graphs.
For the Cai-Fürer-Immerman graphs, for which Torán showed exponential lower bounds for resolution proofs (SAT 2013), we also show that already the global symmetry rule (SRC-I) suffices to allow for polynomial length proofs.
BibTeX - Entry
@InProceedings{schweitzer_et_al:LIPIcs.STACS.2021.58,
author = {Schweitzer, Pascal and Seebach, Constantin},
title = {{Resolution with Symmetry Rule Applied to Linear Equations}},
booktitle = {38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
pages = {58:1--58:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-180-1},
ISSN = {1868-8969},
year = {2021},
volume = {187},
editor = {Bl\"{a}ser, Markus and Monmege, Benjamin},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13703},
URN = {urn:nbn:de:0030-drops-137038},
doi = {10.4230/LIPIcs.STACS.2021.58},
annote = {Keywords: Logical Resolution, Symmetry Rule, Linear Equation System}
}
| Keywords: | Logical Resolution, Symmetry Rule, Linear Equation System | |
| Seminar: | 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 10.03.2021 |
