Mathematical systems theory

, Volume 18, Issue 1, pp 207–235 | Cite as

A combinatorial property of EOL languages

  • A. Ehrenfeucht
  • G. Rozenberg
  • R. Verraedt


Let Δ be an alphabet and II its nontrivial binary partition. Each word over Δ can uniquely be decomposed in subwords (called blocks) consisting of letters of II i only,i ∈ {1,2}. LetK\( \subseteq\) Δ*.K has a long block property (with respect to II), abbreviated asLB-property, if there exists a functionf:N+N+ such that for everywK and every positive integerm the number of blocks of length at mostm inw is bounded byf(m). K has a clustered block property (with respect to II), abbreviated asCB-property, if there exists a positive integerno and a growing functiong:N+N+ such that for everywK and for every positive integerm the blocks of length at mostm can be covered by at mostno segments of length at mostg(m).

It is proved that aCB-property always implies aLB-property but not necessarily other way around. It is proved that an EOL language has aLB-property if and only if it has aCB-property.


Computational Mathematic Combinatorial Property Block Property Binary Partition 
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Copyright information

© Springer-Verlag New York Inc 1985

Authors and Affiliations

  • A. Ehrenfeucht
    • 1
  • G. Rozenberg
    • 2
  • R. Verraedt
    • 3
  1. 1.Department of Computer ScienceUniversity of ColoradoBoulderUSA
  2. 2.Institute of Applied Mathematics and Computer ScienceUniversity of LeidenThe Netherlands
  3. 3.Technical UniversityGroup TBelgium

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