Quantum Algorithm for Dyck Language with Multiple Types of Brackets

We consider the recognition problem of Dyck Language generalized for multiple types brackets. provide an algorithm with quantum query complexity \(O(\sqrt{n}(\log n)^{0.5k})\), where n is length input and k maximal nesting depth Additionally, we show lower bound this which \(\varOmega (\sqrt{n}c^{k})\) some constant c.Interestingly, classical algorithms solving brackets substantially differ from original language. At same time, both kinds language are similar nature requirements.