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A prefix normal word is a binary word with the property that no substring hasmore $1$s than the prefix of the same length. By proving that the set of prefixnormal words is a bubble language, we can exhaustively list all prefix normalwords of length $n$ as a combinatorial Gray code, where successive stringsdiffer by at most two swaps or bit flips. This Gray code can be generated in$\Oh(\log^2 n)$ amortized time per word, while the best generation algorithmhitherto has $\Oh(n)$ running time per word. We also present a membershiptester for prefix normal words, as well as a novel characterization of bubblelanguages.

Generating a Gray code for prefix normal words in amortized polylogarithmic time per word