多类括号Dyck语言的量子算法
Quantum algorithm for Dyck Language with Multiple Types of Brackets
摘要：
我们考虑的识别问题的Dyck语言推广到多种类型的括号。本文给出了一个量子查询复杂度为$O(\sqrt{n}(\log n)^{0.5k})$的算法，其中$n$是输入长度，$k$是括号的最大嵌套深度.此外，我们证明了这个问题的下限是$O(\sqrt{n}c^{k})$的一些常数$c$。有趣的是，解决Dyck语言的多种类型括号的经典算法与解决原始Dyck语言的算法有很大不同。同时，用于求解这两种Dyck语言的量子算法具有相似的性质和要求。
英文摘要：
We consider the recognition problem of the Dyck Language generalized for multiple types of brackets. We provide an algorithm with quantum query complexity $O(\sqrt{n}(\log n)^{0.5k})$, where $n$ is the length of input and $k$ is the maximal nesting depth of brackets. Additionally, we show the lower bound for this problem which is $O(\sqrt{n}c^{k})$ for some constant $c$. Interestingly, classical algorithms solving the Dyck Language for multiple types of brackets substantially differ form the algorithm solving the original Dyck language. At the same time, quantum algorithms for solving both kinds of the Dyck language are of similar nature and requirements.
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。
