Separating LREC from LFP

Anuj Dawar; Felipe Ferreira Santos

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arXiv · 2107.05296

Separating LREC from LFP

Anuj Dawar·Felipe Ferreira Santos

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Abstract

LREC= is an extension of first-order logic with a logarithmic recursion operator. It was introduced by Grohe et al. and shown to capture the complexity class L over trees and interval graphs. It does not capture L in general as it is contained in FPC - fixed-point logic with counting. We show that this containment is strict. In particular, we show that the path systems problem, a classic P-complete problem which is definable in LFP - fixed-point logic - is not definable in LREC= This shows that the logarithmic recursion mechanism is provably weaker than general least fixed points. The proof is based on a novel Spoiler-Duplicator game tailored for this logic.

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Anuj Dawar, Felipe Ferreira Santos. 2021-07-12. Separating LREC from LFP. https://arxiv.org/abs/2107.05296

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