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Real-Time Higher-Order Recursion Schemes

Authors Eric Alsmann , Florian Bruse

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LIPIcs.TIME.2024.16.pdf
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Eric Alsmann
  • University of Kassel, Germany
Florian Bruse
  • University of Kassel, Germany

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Eric Alsmann and Florian Bruse. Real-Time Higher-Order Recursion Schemes. In 31st International Symposium on Temporal Representation and Reasoning (TIME 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 318, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.TIME.2024.16

Abstract

Higher-Order Recursion Schemes (HORS) have long been studied as a tool to model functional programs. Model-checking the tree generated by a HORS of order k against a parity automaton is known to be k-EXPTIME-complete. This paper introduces timed HORS, a real-time version of HORS in the sense of Alur/Dill'90, to be model-checked against a pair of a parity automaton and a timed automaton. We show that adding dense linear time to the notion of recursion schemes adds one exponential to the cost of model-checking, i.e., model-checking a timed HORS of order k can be done in (k+1)-EXPTIME. This is shown by an adaption of the region-graph construction known from the model-checking of timed CTL. We also obtain a hardness result for k = 1, but we strongly conjecture that it holds for all k. This result is obtained by encoding runs of 2-EXPTIME Turing machines into the trees generated by timed HORS.

Subject Classification

ACM Subject Classification
  • Theory of computation → Timed and hybrid models
  • Theory of computation → Tree languages
  • Theory of computation → Automata over infinite objects
Keywords
  • Timed Automata
  • Higher-Order Recursion Schemes
  • Tree Automata

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References

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