LREC= is an extension of first-order logic with a logarithmic recursion operator . It was introduced by Grohe et al. and shown to capture complexityclass 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, aclassic P-complete problem which is definable in LFP – fixed point logic – is not definable .

Author(s) : Anuj Dawar, Felipe Ferreira Santos

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Keywords : logic - lrec - capture - lfp - definable -

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