New Sufficient Algebraic Conditions for Local Consistency over Homogeneous Structures of Finite Duality

Tomáš Nagy; Michael Pinsker; Michał Wrona

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arXiv · 2502.02090

New Sufficient Algebraic Conditions for Local Consistency over Homogeneous Structures of Finite Duality

Tomáš Nagy·Michael Pinsker·Michał Wrona

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Abstract

The path to the solution of Feder-Vardi dichotomy conjecture by Bulatov and Zhuk led through showing that more and more general algebraic conditions imply polynomial-time algorithms for the finite-domain Constraint Satisfaction Problems (CSPs) whose templates satisfy them. These investigations resulted in the discovery of the appropriate height 1 Maltsev conditions characterizing bounded strict width, bounded width, the applicability of the few-subpowers algorithm, and many others. For problems in the range of the similar Bodirsky-Pinsker conjecture on infinite-domain CSPs, one can only find such a characterization for the notion of bounded strict width, with a proof essentially the same as in the finite case. In this paper, we provide the first non-trivial results showing that certain height 1 Maltsev conditions imply bounded width, and in consequence tractability, for a natural subclass of templates within the Bodirsky-Pinsker conjecture which includes many templates in the literature as well as templates for which no complexity classification is known.

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BibTeX RIS

Tomáš Nagy, Michael Pinsker, Michał Wrona. 2025-02-04. New Sufficient Algebraic Conditions for Local Consistency over Homogeneous Structures of Finite Duality. https://arxiv.org/abs/2502.02090

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