带限制分析树电路的拟多项式命中集
Quasi-polynomial Hitting Sets for Circuits with Restricted Parse Trees
摘要：
本文研究了一类非交换非对称电路或唯一解析树（UPT）电路，以及一个相关的少解析树（FewPT）电路模型（最近由Lagarde，Malod和Perifel [LMP 16]和Lagarde，Limaye和Srinivasan [LLS17]介绍）并给出以下结构：（1）UPT电路的拟多项式大小的显式碰集，（2）FewPT电路的拟多项式大小的显式碰集（3）当原像宽度的参数由常数限定时，（已知解析树形状的）UPT电路的多项式大小的显式命中集。上述三个结果是[AGKS 15]，[GKST 15]和[GKS 16]的结果在UPT电路设置上的推广，因此也将它们在交换世界中的结果从只读不经意代数分支程序（ROABP）推广到UPT集多线性电路.主要思想是研究非交换多项式的洗牌，然后可以用来证明UPT电路的适当深度缩减结果，从而允许[AGKS 15]，[GKST 15]和[GKS 16]中的思想的仔细翻译。
英文摘要：
We study the class of non-commutative Unambiguous circuits or Unique-Parse-Tree (UPT) circuits, and a related model of Few-Parse-Trees (FewPT) circuits (which were recently introduced by Lagarde, Malod and Perifel [LMP16] and Lagarde, Limaye and Srinivasan [LLS17]) and give the following constructions: (1) An explicit hitting set of quasipolynomial size for UPT circuits, (2) An explicit hitting set of quasipolynomial size for FewPT circuits (circuits with constantly many parse tree shapes), (3) An explicit hitting set of polynomial size for UPT circuits (of known parse tree shape), when a parameter of preimage-width is bounded by a constant. The above three results are extensions of the results of [AGKS15], [GKST15] and [GKS16] to the setting of UPT circuits, and hence also generalize their results in the commutative world from read-once oblivious algebraic branching programs (ROABPs) to UPT-set-multilinear circuits. The main idea is to study shufflings of non-commutative polynomials, which can then be used to prove suitable depth reduction results for UPT circuits and thereby allow a careful translation of the ideas in [AGKS15], [GKST15] and [GKS16].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
