Mathematical systems theory

, Volume 22, Issue 1, pp 151–159 | Cite as

Cardinality problems of compositions of morphisms and inverse morphisms

  • T. Harju
  • H. C. M. Kleijn


We show that we cannot effectively determine whether, for morphismsα i ,β i ,card ( 0 −1 α1) =card( 0 −1 β1) for all wordsu over the domain alphabets of the two given compositions. In contrast it is decidable for morphismsα i ,β i and a regular setR whethercard(0α 1 −1 ) =card(0β 1 −1 ) for all wordsu inR. In order to prove the latter result we give a characterization of the multiplicity functions of simple finite automata by using cardinalities of compositions of the above form. Finally, we show that the above decidability result also holds when we consider rational functions rather than morphisms.


Rational Function Computational Mathematic Decidability Result Finite Automaton Regular setR 
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Copyright information

© Springer-Verlag New York Inc 1989

Authors and Affiliations

  • T. Harju
    • 1
  • H. C. M. Kleijn
    • 2
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland
  2. 2.Department of Computer ScienceLeiden UniversityLeidenThe Netherlands

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