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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)

Abstract

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.

Keywords

Module Specification Language Maximal Order Type Fixed Point Varieties Tail Recursion Recursion Depth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

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