Weak but Not Strong Asymptotic Testability

Senhan Yao

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arXiv · 2607.26476

Weak but Not Strong Asymptotic Testability

Senhan Yao

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Abstract

We construct two fixed disjoint families $H_0,H_1$ of stationary ergodic binary process distributions for which a weakly asymptotically consistent test exists, but no strongly asymptotically consistent test exists. The construction combines a synchronizing binary suspension code, an independent i.i.d marker process, and countably many independent slowly switching two-state Markov chains. In particular, this disproves the asymptotic-consistency branch of a conjecture of Ryabko.

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Senhan Yao. 2026-07-29. Weak but Not Strong Asymptotic Testability. https://arxiv.org/abs/2607.26476

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