Harwath, Frederik and Heimberg, Lucas and Schweikardt, Nicole - Preservation and decomposition theorems for bounded degree structures

lmcs:1618 - Logical Methods in Computer Science, December 29, 2015, Volume 11, Issue 4
Preservation and decomposition theorems for bounded degree structures

Authors: Harwath, Frederik and Heimberg, Lucas and Schweikardt, Nicole

We provide elementary algorithms for two preservation theorems for first-order sentences (FO) on the class \^ad of all finite structures of degree at most d: For each FO-sentence that is preserved under extensions (homomorphisms) on \^ad, a \^ad-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 \^ad-equivalent Feferman-Vaught decomposition can be computed in 3-fold exponential time. We also provide a matching lower bound.


Source : oai:arXiv.org:1511.05888
DOI : 10.2168/LMCS-11(4:17)2015
Volume: Volume 11, Issue 4
Published on: December 29, 2015
Submitted on: August 11, 2016
Keywords: Computer Science - Logic in Computer Science


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