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

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Author:Frederik Harwath, Lucas Heimberg, Nicole Schweikardt
ArXiv Id:
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
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
Page Number:44
First Page:1
Last Page:44
Creative Commons
Institutes:Informatik und Mathematik / Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoCreative Commons - Namensnennung-Keine Bearbeitung