Re-pairing brackets
Dmitry V. Chistikov, M. Vyalyi · 2020
Consider the following one-player game. Take a well-formed sequence of opening and closing brackets (a Dyck word). As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the entire sequence, and the cost of a strategy is measured by its width: the maximum number of nonempty segments of symbols (separated by blank space) seen during the play.