用于字典序最小字符串旋转的量子算法
Quantum Algorithm for Lexicographically Minimal String Rotation
AI总结：
本文提出求解字典序最小字符串旋转的O(n^{3/4})量子查询算法，平均复杂度达渐近最优，且优于经典随机算法，可应用于苯环识别等场景。
摘要：
字典序最小字符串旋转（LMSR）是在字符串的所有旋转结果中找出字典序最小结果的问题，广泛应用于图、多边形、自动机和化学结构的等价性检验。本文提出一种求解LMSR的O(n^{3/4})量子查询算法。该算法的平均情况查询复杂度为O(√n log n)，与其Ω(√(n/log n))的下界相比，在至多相差一个多对数因子的意义下是渐近最优的。此外，我们证明该量子算法在最坏情况和平均情况下均优于所有（经典）随机算法。作为应用，该算法可用于苯环识别和不相交环自动机最小化。
英文摘要：
Lexicographically minimal string rotation (LMSR) is a problem to find the minimal one among all rotations of a string in the lexicographical order, which is widely used in equality checking of graphs, polygons, automata and chemical structures. In this paper, we propose an $O(n^{3/4})$ quantum query algorithm for LMSR. In particular, the algorithm has average-case query complexity $O(\sqrt n \log n)$, which is shown to be asymptotically optimal up to a polylogarithmic factor, compared to its $Ω\left(\sqrt{n/\log n}\right)$ lower bound. Furthermore, we show that our quantum algorithm outperforms any (classical) randomized algorithms in both worst and average cases. As an application, it is used in benzenoid identification and disjoint-cycle automata minimization.
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。
