English

On the Expressive Power of Higher-Order Pushdown Systems

Formal Languages and Automata Theory 2023-06-22 v2

Abstract

We show that deterministic collapsible pushdown automata of second order can recognize a language that is not recognizable by any deterministic higher-order pushdown automaton (without collapse) of any order. This implies that there exists a tree generated by a second order collapsible pushdown system (equivalently, by a recursion scheme of second order) that is not generated by any deterministic higher-order pushdown system (without collapse) of any order (equivalently, by any safe recursion scheme of any order). As a side effect, we present a pumping lemma for deterministic higher-order pushdown automata, which potentially can be useful for other applications.

Keywords

Cite

@article{arxiv.2008.00650,
  title  = {On the Expressive Power of Higher-Order Pushdown Systems},
  author = {Paweł Parys},
  journal= {arXiv preprint arXiv:2008.00650},
  year   = {2023}
}
R2 v1 2026-06-23T17:35:31.061Z