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Lambda-Definable Order-3 Tree Functions are Well-Quasi-Ordered

Authors Kazuyuki Asada , Naoki Kobayashi



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Author Details

Kazuyuki Asada
  • Tohoku University, Sendai, Japan
Naoki Kobayashi
  • The University of Tokyo, Tokyo, Japan

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Kazuyuki Asada and Naoki Kobayashi. Lambda-Definable Order-3 Tree Functions are Well-Quasi-Ordered. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 14:1-14:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FSTTCS.2018.14

Abstract

Asada and Kobayashi [ICALP 2017] conjectured a higher-order version of Kruskal's tree theorem, and proved a pumping lemma for higher-order languages modulo the conjecture. The conjecture has been proved up to order-2, which implies that Asada and Kobayashi's pumping lemma holds for order-2 tree languages, but remains open for order-3 or higher. In this paper, we prove a variation of the conjecture for order-3. This is sufficient for proving that a variation of the pumping lemma holds for order-3 tree languages (equivalently, for order-4 word languages).

Subject Classification

ACM Subject Classification
  • Theory of computation → Lambda calculus
Keywords
  • higher-order grammar
  • pumping lemma
  • Kruskal's tree theorem
  • well-quasi-ordering
  • simply-typed lambda calculus

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References

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