Preservation and decomposition theorems for bounded degree structures
- We provide elementary algorithms for two preservation theorems for first-order sentences (FO) on the class ℭd of all finite structures of degree at most d: For each FO-sentence that is preserved under extensions (homomorphisms) on ℭd, a ℭd-equivalent existential (existential-positive) FO-sentence can be constructed in 5-fold (4-fold) exponential time. This is complemented by lower bounds showing that a 3-fold exponential blow-up of the computed existential (existential-positive) sentence is unavoidable. Both algorithms can be extended (while maintaining the upper and lower bounds on their time complexity) to input first-order sentences with modulo m counting quantifiers (FO+MODm). Furthermore, we show that for an input FO-formula, a ℭd-equivalent Feferman-Vaught decomposition can be computed in 3-fold exponential time. We also provide a matching lower bound
| Author: | Frederik Harwath, Lucas Heimberg, Nicole Schweikardt |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-306349 |
| DOI: | https://doi.org/10.2168/LMCS-11(4:17)2015 |
| ISSN: | 1860-5974 |
| ArXiv Id: | http://arxiv.org/abs/1511.05888 |
| Parent Title (German): | Logical Methods in Computer Science |
| Publisher: | Department of Theoretical Computer Science, Technical University of Braunschweig |
| Place of publication: | Braunschweig |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2015/12/29 |
| Date of first Publication: | 2015/12/29 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2016/06/16 |
| Volume: | 11 |
| Issue: | 4:17 |
| Page Number: | 44 |
| First Page: | 1 |
| Last Page: | 44 |
| Note: | Creative Commons http://creativecommons.org/licenses/by-nd/2.0/ |
| HeBIS-PPN: | 425322963 |
| Institutes: | Informatik und Mathematik / Informatik |
| Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung-Keine Bearbeitung |
