English

Disproving Termination of Non-Erasing Sole Combinatory Calculus with Tree Automata (Full Version)

Logic in Computer Science 2024-06-21 v1 Formal Languages and Automata Theory

Abstract

We study the termination of sole combinatory calculus, which consists of only one combinator. Specifically, the termination for non-erasing combinators is disproven by finding a desirable tree automaton with a SAT solver as done for term rewriting systems by Endrullis and Zantema. We improved their technique to apply to non-erasing sole combinatory calculus, in which it suffices to search for tree automata with a final sink state. Our method succeeds in disproving the termination of 8 combinators, whose termination has been an open problem.

Keywords

Cite

@article{arxiv.2406.14305,
  title  = {Disproving Termination of Non-Erasing Sole Combinatory Calculus with Tree Automata (Full Version)},
  author = {Keisuke Nakano and Munehiro Iwami},
  journal= {arXiv preprint arXiv:2406.14305},
  year   = {2024}
}

Comments

This is the full version of the corresponding CIAA 2024 paper