Preservation and decomposition theorems for bounded degree structures

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2014-07-14 DOI:10.1145/2603088.2603130

Frederik Harwath, Lucas Heimberg, Nicole Schweikardt

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引用次数: 14

Abstract

We provide elementary algorithms for two preservation theorems for first-order sentences with modulo m counting quantifiers (FO+MODm) on the class Cd of all finite structures of degree at most d: For each FO+MODm-sentence that is preserved under extensions (homomorphisms) on Cd, a Cd-equivalent existential (existential-positive) FO-sentence can be constructed in 6-fold (4-fold) exponential time. For FO-sentences, the algorithm has 5-fold (4-fold) exponential time complexity. This is complemented by lower bounds showing that for FO-sentences a 3-fold exponential blow-up of the computed existential (existential-positive) sentence is unavoidable. 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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有界度结构的保存与分解定理

我们提供了两个保留定理的初等算法，这些定理适用于所有次不超过d的有限结构的Cd类上具有模m计数量词的一阶句(FO+MODm):对于每个在Cd上的扩展(同态)下保留的FO+MODm-句，可以在6倍(4倍)指数时间内构造一个Cd-等价的存在(存在-正)FO-句。对于o句，该算法具有5倍(4倍)指数时间复杂度。这是下界的补充，表明对于o句，计算存在(存在-肯定)句的3倍指数膨胀是不可避免的。此外，我们证明了对于一个输入fo公式，一个等效cd的Feferman-Vaught分解可以在3倍指数时间内计算出来。我们还提供了一个匹配的下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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