We study the problem of testing forbidden patterns. The patterns that are of significant interest include monotone pattern and $(1,3,2)$-pattern. For the problem of testing monotone patterns, \cite{newman2019testing} propose a non-adaptive algorithm with query complexity $(\log n)^{O(k^2)}$. \cite{ben2019finding} then improve the query complexity of non-adaptive algorithm to $\Omega((\log n)^{\lfloor\log k\rfloor})$. Further, \cite{ben2019optimal} propose an adaptive algorithm for testing monotone pattern with optimal query complexity $O(\log n)$. However, the adaptive algorithm and the analysis are rather complicated. We provide a simple adaptive algorithm with one-sided error for testing monotone permutation. We also present an algorithm with improved query complexity for testing $(1,3,2)$-pattern.

中文翻译：

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用于排列测试的改进算法

我们研究测试禁止模式的问题。重要的模式包括单调模式和 $(1,3,2)$-pattern。针对单调模式的测试问题，\cite{newman2019testing}提出了一种查询复杂度为$(\log n)^{O(k^2)}$的非自适应算法。\cite{ben2019finding} 然后将非自适应算法的查询复杂度提高到 $\Omega((\log n)^{\lfloor\log k\rfloor})$。此外，\cite{ben2019optimal} 提出了一种自适应算法，用于测试具有最优查询复杂度 $O(\log n)$ 的单调模式。但是，自适应算法和分析比较复杂。我们提供了一种简单的自适应算法，用于测试单调排列的单边误差。我们还提出了一种改进了查询复杂度的算法来测试 $(1,3,2)$-pattern。