AI 中文总结
该研究解决了Alon等人的问题，定量刻画了稠密图模型中与规模无关的单侧可测试性，建立了其与超图容器的等价性，可扩展至多类结构并给出应用结果。
AI 中文摘要
我们针对稠密图模型中与规模无关的单侧可测试性，给出了定量组合刻画，解决了Alon、Fischer、Newman和Shapira提出的问题。对于遗传图性质，我们证明单侧可测试性在定量上等价于合适超图容器的存在性，超图容器是现代组合学中核心且广泛使用的工具。将该等价性与Alon-Shapira的半遗传性概念结合，可得到任意图性质的定量刻画。该对应关系双向有效，能在测试器复杂度与容器参数间提供显式转换。我们的证明无正则性条件，且可一致扩展到每个固定的有界元有限关系签名，包括有向图、着色图和超图。作为应用，我们得到了划分性质的定量闭包结果，以及由存在线性规模大的诱导子结构定义的性质的测试器。
英文摘要
We give a quantitative combinatorial characterization of size-oblivious one-sided testability in the dense graph model, resolving a question of Alon, Fischer, Newman, and Shapira. For hereditary graph properties, we prove that one-sided testability is quantitatively equivalent to the existence of suitable hypergraph containers, a central and widely used tool in modern combinatorics. Combining this equivalence with the Alon-Shapira notion of semi-hereditariness yields a quantitative characterization of arbitrary graph properties. The correspondence is effective in both directions and provides explicit translations between tester complexity and container parameters. Our proof is regularity-free and extends uniformly to every fixed finite relational signature of bounded arity, including digraphs, coloured graphs, and hypergraphs. As applications, we obtain quantitative closure results for partition properties and testers for properties defined by the existence of a linearly large induced substructure.
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