Quantum algorithm for Dyck Language with Multiple Types of Brackets

TL;DR

This paper introduces a quantum algorithm for recognizing generalized Dyck languages with multiple bracket types, achieving specific query complexities and establishing lower bounds, thus advancing quantum language recognition methods.

Contribution

It presents a novel quantum algorithm for the generalized Dyck language with multiple brackets and analyzes its complexity and lower bounds, highlighting similarities with classical approaches.

Findings

Quantum algorithm with $O(\sqrt{n}(\log n)^{0.5k})$ query complexity

Lower bound of $O(\sqrt{n}c^{k})$ for the problem

Quantum algorithms for Dyck languages of different types are similar in nature

Abstract

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.