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arXiv · 2511.02596

Characterizing the Exponential-Space Hierarchy Via Partial Fixpoints

Florian Bruse·David Kronenberger·Martin Lange
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Abstract

The characterization of PSPACE-queries over ordered structures as exactly those expressible in first-order logic with partial fixpoints (Vardi'82) is one of the classical results in the field of descriptive complexity. In this paper, we extend this result to characterizations of k-EXPSPACE-queries for arbitrary k, characterizing them as exactly those expressible in order-k+1-higher-order logic with partial fixpoints. For k>1, the restriction to ordered structures is no longer necessary due to the high expressive power of higher-order logic.

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Florian Bruse, David Kronenberger, Martin Lange. 2025-11-04. Characterizing the Exponential-Space Hierarchy Via Partial Fixpoints. https://doi.org/10.4204/eptcs.435.7

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