English

Pumping Lemma for Higher-order Languages

Formal Languages and Automata Theory 2017-05-31 v1

Abstract

We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given language does not belong to the classes of regular/context-free/indexed languages. We prove a pumping lemma for word/tree languages of arbitrary orders, modulo a conjecture that a higher-order version of Kruskal's tree theorem holds. We also show that the conjecture indeed holds for the order-2 case, which yields a pumping lemma for order-2 tree languages and order-3 word languages.

Keywords

Cite

@article{arxiv.1705.10699,
  title  = {Pumping Lemma for Higher-order Languages},
  author = {Kazuyuki Asada and Naoki Kobayashi},
  journal= {arXiv preprint arXiv:1705.10699},
  year   = {2017}
}

Comments

ICALP 2017

R2 v1 2026-06-22T20:03:43.149Z