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arXiv · 2407.13339

On the complexity of Maslov's class $\overline{\text{K}}$

Oskar Fiuk·Emanuel Kieronski·Vincent Michielini
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Abstract

Maslov's class $\overline{\text{K}}$ is an expressive fragment of First-Order Logic known to have decidable satisfiability problem, whose exact complexity, however, has not been established so far. We show that $\overline{\text{K}}$ has the exponential-sized model property, and hence its satisfiability problem is NExpTime-complete. Additionally, we get new complexity results on related fragments studied in the literature, and propose a new decidable extension of the uniform one-dimensional fragment (without equality). Our approach involves a use of satisfiability games tailored to $\overline{\text{K}}$ and a novel application of paradoxical tournament graphs.

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Oskar Fiuk, Emanuel Kieronski, Vincent Michielini. 2024-07-18. On the complexity of Maslov's class $\overline{\text{K}}$. https://arxiv.org/abs/2407.13339

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