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Generating a Gray code for prefix normal words in amortized polylogarithmic time per word
journal contributionposted on 26.06.2020, 14:54 by Peter Burcsi, Gabriele Fici, Zsuzsanna Liptak, Rajeev Raman, Joe Sawada
A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal words of length nas a combinatorial Gray code, where successive strings differ by at most two swaps or bit flips. This Gray code can be generated in O (log2n) amortized time per word, while the best generation algorithm hither to has O (n) running time per word. We also present a membership tester for prefix normal words, as well as a novel characterization of bubble languages.