Acta Informatica

, Volume 50, Issue 3, pp 157–173 | Cite as

Avoiding cross-bifix-free binary words

  • Stefano Bilotta
  • Elisabetta Grazzini
  • Elisa Pergola
  • Renzo Pinzani
Original Article


In this paper we study the construction and the enumeration of binary words in \(\{0,1\}^*\) having more 1’s than 0’s and avoiding a set of cross-bifix-free patterns. We give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. Moreover, the problem of associating a word to a path in the generating tree obtained by the succession rule is solved by introducing an algorithm which constructs all binary words having more 1’s than 0’s and then kills those containing the forbidden patterns. Finally, we give the generating function of such words according to the number of ones.


Generate Tree Intrusion Detection Lattice Path Access Control Model Catalan Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stefano Bilotta
    • 1
  • Elisabetta Grazzini
    • 1
  • Elisa Pergola
    • 1
  • Renzo Pinzani
    • 1
  1. 1.Dipartimento di Sistemi e InformaticaUniversità degli Studi di Firenze FirenzeItaly

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