A read-once oblivious arithmetic branching program (ROABP) is an arithmetic branching program (ABP) where each variable occurs in at most one layer. We give the first polynomial-time whitebox identity test for a polynomial computed by a sum of constantly many ROABPs. We also give a corresponding blackbox algorithm with quasi-polynomial-time complexity $${n^{O({\rm log}\,n)}}$$nO(logn). In both the cases, our time complexity is double exponential in the number of ROABPs.ROABPs are a generalization of set-multilinear depth-3 circuits. The prior results for the sum of constantly many set-multilinear depth-3 circuits were only slightly better than brute force, i.e., exponential time. Our techniques are a new interplay of three concepts for ROABP: low evaluation dimension, basis isolating weight assignment and low-support rank concentration. We relate basis isolation to rank concentration and extend it to a sum of two ROABPs using evaluation dimension.

中文翻译：

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Read-Once Oblivious 算术分支程序总和的确定性身份测试

一次读取不经意算术分支程序 (ROABP) 是一种算术分支程序 (ABP)，其中每个变量最多出现在一层。我们给出了一个多项式的第一个多项式时间白盒恒等式测试，该多项式是由许多 ROABP 的总和计算出来的。我们还给出了相应的具有拟多项式时间复杂度 $${n^{O({\rm log}\,n)}}$$nO(logn) 的黑盒算法。在这两种情况下，我们的时间复杂度都是 ROABP 数量的双指数。ROABP 是 set-multilinear depth-3 电路的推广。先前的结果是不断地许多 set-multilinear depth-3 电路的总和，仅略好于蛮力，即指数时间。我们的技术是 ROABP 三个概念的新相互作用：低评估维度、基础隔离权重分配和低支持等级集中。