可视下推语言的流性质测试
Streaming Property Testing of Visibly Pushdown Languages
摘要：
在语言识别的背景下，我们证明了流属性测试程序对流算法和属性测试程序的优越性，当它们不相结合时。由Feigenbaum等人发起，流式特性测试器是在特性测试近似下识别语言的流式算法：它必须将语言的输入与那些远离它的$\varepsilon$区分开，同时使用最小可能的存储器（而不是限制其输入查询的数量）。我们的主要结果是一个流$\varepsilon$ -属性测试明显下推语言（VPL）与单侧错误使用内存空间$\mathrm{poly}((\log n) / \varepsilon)$。这种结构依赖于一个（非流）属性测试仪加权正则语言的基础上，以前的测试仪由阿隆等人。我们提供了一个简单的应用程序，这个测试仪流测试特殊情况下的VPL已经很难流算法和属性测试。我们的主要算法是一个原始的模拟相结合的明显下推自动机使用堆栈的高度小，但可能的线性大小的项目。在第二步中，这些项目被小草图取代。这些草图依赖于我们引入的后缀采样的概念。这种采样是将我们的流测试器算法连接到属性测试器的关键思想。
英文摘要：
In the context of language recognition, we demonstrate the superiority of streaming property testers against streaming algorithms and property testers, when they are not combined. Initiated by Feigenbaum et al., a streaming property tester is a streaming algorithm recognizing a language under the property testing approximation: it must distinguish inputs of the language from those that are $\varepsilon$-far from it, while using the smallest possible memory (rather than limiting its number of input queries). Our main result is a streaming $\varepsilon$-property tester for visibly pushdown languages (VPL) with one-sided error using memory space $\mathrm{poly}((\log n) / \varepsilon)$. This constructions relies on a (non-streaming) property tester for weighted regular languages based on a previous tester by Alon et al. We provide a simple application of this tester for streaming testing special cases of instances of VPL that are already hard for both streaming algorithms and property testers. Our main algorithm is a combination of an original simulation of visibly pushdown automata using a stack with small height but possible items of linear size. In a second step, those items are replaced by small sketches. Those sketches relies on a notion of suffix-sampling we introduce. This sampling is the key idea connecting our streaming tester algorithm to property testers.
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