Absoluteness of subword inequality is undecidable

TL;DR

This paper proves that determining whether a subword history is always non-negative across all words over an alphabet is an undecidable problem, resolving an open question in formal language theory.

Contribution

The paper establishes the undecidability of the absolute non-negativity problem for subword histories, even under stronger conditions than previously considered.

Findings

Proves the undecidability of the subword inequality absoluteness problem.

Extends previous results by showing undecidability under more restrictive conditions.

Answers an open question posed by Mateescu, Salomaa, and Yu.

Abstract

Mateescu, Salomaa, and Yu asked: is it decidable whether a given subword history assumes only non-negative values for all words over a given alphabet. In this paper, we solve this open problem by proving that this problem is undecidable even under stronger conditions than supposed originally.