DeepAI AI Chat
Log In Sign Up

Quantum algorithm for Dyck Language with Multiple Types of Brackets

06/17/2021
by   Kamil Khadiev, et al.
0

We consider the recognition problem of the Dyck Language generalized for multiple types of brackets. We provide an algorithm with quantum query complexity O(√(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(√(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.

READ FULL TEXT

page 1

page 2

page 3

page 4

12/04/2019

Quantum Query Complexity of Dyck Languages with Bounded Height

We consider the problem of determining if a sequence of parentheses is w...
07/17/2019

Almost tight bound on the query complexity of generalized Simon's problem

Simon's problem played an important role in the history of quantum algor...
05/28/2020

Classical and Quantum Algorithms for Constructing Text from Dictionary Problem

We study algorithms for solving the problem of constructing a text (long...
06/25/2019

Quantum speedup of branch-and-bound algorithms

Branch-and-bound is a widely used technique for solving combinatorial op...
07/06/2020

Quantum Lower and Upper Bounds for 2D-Grid and Dyck Language

We study the quantum query complexity of two problems. First, we consi...
11/29/2022

The Adversary Bound Revisited: From Optimal Query Algorithms to Optimal Control

This note complements the paper "One-Way Ticket to Las Vegas and the Qua...
02/18/2022

Quantum and Classical Algorithms for Bounded Distance Decoding

In this paper, we provide a comprehensive overview of a recent debate ov...