Deciding Quantifier-free Definability in Finite Algebraic Structures

Q3 Computer Science

Electronic Notes in Theoretical Computer Science Pub Date : 2020-03-01 DOI:10.1016/j.entcs.2020.02.003

Miguel Campercholi, Mauricio Tellechea, Pablo Ventura

引用次数: 0

Abstract

This work deals with the definability problem by quantifier-free first-order formulas over a finite algebraic structure. We show the problem to be coNP-complete and present a decision algorithm based on a semantical characterization of definable relations as those preserved by isomorphisms of substructures. Our approach also includes the design of an algorithm that computes the isomorphism type of a tuple in a finite algebraic structure. Proofs of soundness and completeness of the algorithms are presented, as well as empirical tests assessing their performances.

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有限代数结构中无量词可定义性的确定

本文研究有限代数结构上无量词一阶公式的可定义性问题。我们证明了这个问题是conp完备的，并提出了一种基于可定义关系的语义表征的决策算法，这些可定义关系是由子结构的同构保存的。我们的方法还包括设计一种算法来计算有限代数结构中元组的同构类型。提出了算法的可靠性和完整性的证明，以及评估其性能的经验测试。

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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Electronic Notes in Theoretical Computer Science Computer Science-Computer Science (all)

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