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- W3030407714 abstract "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. For various initial sequences, we prove upper and lower bounds on the minimum width sufficient for re-pairing. (In particular, the sequence associated with the complete binary tree of height n admits a strategy of width sub-exponential in log n.) Our two key contributions are (1) lower bounds on the width and (2) their application in automata theory: quasi-polynomial lower bounds on the translation from one-counter automata to Parikh-equivalent nondeterministic finite automata. The latter result answers a question by Atig et al. (2016)." @default.
- W3030407714 created "2020-06-05" @default.
- W3030407714 creator A5054888158 @default.
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- W3030407714 date "2020-07-08" @default.
- W3030407714 modified "2023-10-16" @default.
- W3030407714 title "Re-pairing brackets" @default.
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- W3030407714 doi "https://doi.org/10.1145/3373718.3394752" @default.
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