Characterizing the Exponential-Space Hierarchy Via Partial Fixpoints
By: Florian Bruse, David Kronenberger, Martin Lange
Potential Business Impact:
Makes computers solve harder problems faster.
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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