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DOI: 10.4230/LIPIcs.ITCS.2017.27
URN: urn:nbn:de:0030-drops-81435
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8143/
Rossman, Benjamin
An Improved Homomorphism Preservation Theorem From Lower Bounds in Circuit Complexity
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Abstract
Previous work of the author [Rossmann'08] showed that the Homomorphism Preservation Theorem of classical model theory remains valid when its statement is restricted to finite structures. In this paper, we give a new proof of this result via a reduction to lower bounds in circuit complexity, specifically on the AC0 formula size of the colored subgraph isomorphism problem. Formally, we show the following: if a first-order sentence of quantifier-rank k is preserved under homomorphisms on finite structures, then it is equivalent on finite structures to an existential-positive sentence of quantifier-rank poly(k). Quantitatively, this improves the result of [Rossmann'08], where the upper bound on quantifier-rank is a non-elementary function of k.
BibTeX - Entry
@InProceedings{rossman:LIPIcs:2017:8143,
author = {Benjamin Rossman},
title = {{An Improved Homomorphism Preservation Theorem From Lower Bounds in Circuit Complexity}},
booktitle = {8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
pages = {27:1--27:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-029-3},
ISSN = {1868-8969},
year = {2017},
volume = {67},
editor = {Christos H. Papadimitriou},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8143},
URN = {urn:nbn:de:0030-drops-81435},
doi = {10.4230/LIPIcs.ITCS.2017.27},
annote = {Keywords: circuit complexity, finite model theory}
}
| Keywords: | circuit complexity, finite model theory | |
| Seminar: | 8th Innovations in Theoretical Computer Science Conference (ITCS 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 28.11.2017 |
