Choiceless Logarithmic Space

Grädel, Erich; Schalthöfer, Svenja

doi:10.4230/lipics.mfcs.2019.31

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2021

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“…It is known that LREC = does not capture L on all graphs. In particular, LREC = is included in FPC and the CFI construction that separates FPC from P can be suitably padded to give a separation of LREC = from L [8]. While Grohe et al proved that LREC is properly contained in FPC (for instance, it cannot express reachability on undirected graphs), the question was left open for the stronger logic LREC = .…”

Section: Introductionmentioning

confidence: 99%

Separating LREC from LFP

Dawar,

Santos

2021

Preprint

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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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Section: Introductionmentioning

confidence: 99%