Two-way affine automata can verify every language
Formal Languages and Automata Theory
2025-02-19 v1
Abstract
When used as verifiers in Arthur-Merlin systems, two-way quantum finite automata can verify membership in all languages with bounded error with double-exponential expected running time, which cannot be achieved by their classical counterparts. We obtain the same result for affine automata with single-exponential expected time. We show that every binary (and r-ary) language is verified by some two-way affine finite automata verifiers by presenting two protocols: A weak verification protocol uses a single affine register and the input is read once; and, a strong verification protocol uses two affine registers. These results reflects the remarkable verification capabilities of affine finite automata.
Keywords
Cite
@article{arxiv.2502.12879,
title = {Two-way affine automata can verify every language},
author = {Zeyu Chen and Abuzer Yakaryılmaz},
journal= {arXiv preprint arXiv:2502.12879},
year = {2025}
}