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arXiv · 2303.17017

Two algorithms to decide Quantifier-free Definability in Finite Algebraic Structures

Miguel Campercholi·Mauricio Tellechea·Pablo Ventura
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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 two decision algorithms based on a semantical characterization of definable relations as those preserved by isomorphisms of substructures, the second one also providing a formula in the positive case. 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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Miguel Campercholi, Mauricio Tellechea, Pablo Ventura. 2023-03-29. Two algorithms to decide Quantifier-free Definability in Finite Algebraic Structures. https://arxiv.org/abs/2303.17017

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