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arXiv · 2406.14305

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

Keisuke Nakano·Munehiro Iwami
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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.

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Keisuke Nakano, Munehiro Iwami. 2024-06-20. Disproving Termination of Non-Erasing Sole Combinatory Calculus with Tree Automata (Full Version). https://arxiv.org/abs/2406.14305

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