Year: 2026
Type: preprint
Abstract: For two distinct binary words of length $n$, the separating words problem asks for a small deterministic finite automaton that accepts exactly one of them. Chase proved a $\widetilde O(n^{1/3})$ upper bound using a complex-analytic estimate for sparse polynomials. We replace that estimate by a finite-difference argument and a second-order real recurrence cutoff. The resulting elementary proof gives an explicit bound of $O(n^{1/3}(\log n)^{7/3})$ states.
Source: arXiv (Cornell University)
Author: Xu, Chen
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212020963