Space-Efficient Fragments of Higher-Order Fixpoint Logic

  • Florian BruseEmail author
  • Martin Lange
  • Etienne Lozes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10506)


Higher-Order Fixpoint Logic (HFL) is a modal specification language whose expressive power reaches far beyond that of Monadic Second-Order Logic, achieved through an incorporation of a typed \(\lambda \)-calculus into the modal \(\mu \)-calculus. Its model checking problem on finite transition systems is decidable, albeit of high complexity, namely k-EXPTIME-complete for formulas that use functions of type order at most \(k > 0\). In this paper we present a fragment with a presumably easier model checking problem. We show that so-called tail-recursive formulas of type order k can be model checked in \((k-1)\)-EXPSPACE, and also give matching lower bounds. This yields generic results for the complexity of bisimulation-invariant non-regular properties, as these can typically be defined in HFL.


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Authors and Affiliations

  1. 1.University of KasselKasselGermany
  2. 2.LSV, ENS Paris-Saclay, CNRSCachanFrance

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