We give improved and almost optimal testers for several classes of Boolean functions on $n$ inputs that have concise representation in the uniform and distribution-free model. Classes, such as $k$-junta, $k$-linear functions, $s$-term DNF, $s$-term monotone DNF, $r$-DNF, decision list, $r$-decision list, size-$s$ decision tree, size-$s$ Boolean formula, size-$s$ branching programs, $s$-sparse polynomials over the binary field and function with Fourier degree at most $d$. The method can be extended to several other classes of functions over any domain that can be approximated by functions that have a small number of relevant variables.

翻译：我们针对均匀分布和无分布模型下具有简洁表示的几类$n$输入布尔函数，给出了改进且近乎最优的测试器。这些函数类包括：$k$-junta、$k$-线性函数、$s$-项DNF、$s$-项单调DNF、$r$-DNF、决策列表、$r$-决策列表、规模为$s$的决策树、规模为$s$的布尔公式、规模为$s$的分支程序、二元域上的$s$-稀疏多项式以及傅里叶度数至多为$d$的函数。该方法可推广至任意定义域上能被少量相关变量函数逼近的其他几类函数。