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A note on intersections of free submonoids of a free monoid

  • Juhani Karhumäki
Conference paper
  • 94 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 154)

Abstract

According to a theorem of Tilson [7] any intersection of free submonoids of a free monoid is free. Here we consider intersections of the form {x,y}* ∩ {u,v}*, where x,y,u and v are words in a finitely generated free monoid ⌆*, and show that if both the monoids {x,y}* and {u,v* are of the rank two, then the intersection is a free monoid generated either by (at most) two words or by a regular language of the form Β0+Β(γ(1+δ+...+δt))*ɛ for some words Β0, Β, γ, δ and ɛ, and some integer t⩾0. An example is given showing that the latter possibility may occur for each t⩾0 with nonempty values of the words. If {x,y} and {u,v} are prefixes then necessarily t=0 and Β0=1.

Keywords

Atomic Solution Regular Language Free Monoid Formal Language Theory Infinite Word 
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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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Juhani Karhumäki
    • 1
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland

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