Separating LREC from LFP

Abstract

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 —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 —fixed-point logic—is not definable in . This shows that the logarithmic recursion mechanism is provably weaker than general least fixed points.