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Bubble-Flip—A New Generation Algorithm for Prefix Normal Words

  • Ferdinando Cicalese
  • Zsuzsanna Lipták
  • Massimiliano Rossi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10792)

Abstract

We present a new recursive generation algorithm for prefix normal words. These are binary words with the property that no factor has more 1s than the prefix of the same length. The new algorithm uses two operations on binary words, which exploit certain properties of prefix normal words in a smart way. We introduce infinite prefix normal words and show that one of the operations used by the algorithm, if applied repeatedly to extend the word, produces an ultimately periodic infinite word, which is prefix normal and whose period’s length and density we can predict from the original word.

Keywords

Algorithms on automata and words Combinatorics on words Combinatorial generation Prefix normal words Infinite words Binary languages 

Notes

Acknowledgements

We wish to thank three anonymous referees, who read our paper very carefully and whose detailed comments contributed to improving its exposition.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversity of VeronaVeronaItaly

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