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Transitive orientations, möbius functions, and complete semi-thue systems for free partially commutative monoids

  • Volker Diekert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)

Abstract

Let I\(\subseteq\)X×X be an independence relation over a finite alphabet X and M=X*/{(ab, ba)|(a, b)teI} the associated free partially commutative monoid. The Möbius function of M is a polynomial in the ring of formal power series ZM》. Taking representatives we may view it as a polynomial in ZX*》. We call it unambiguous if its formal inverse in ZX*》 is the characteristic series over a set of representatives of M. The main result states that there is an unambiguous Möbius function of M in ZX*》 if and only if there is a transitive orientation of I. It is known that transitive orientations correspond exactly to finite complete semi-Thue systems S\(\subseteq\)XX* which define M. We obtain a one-to-one correspondence between unambiguous Möbius functions, transitive orientations and finite (normalized) complete semi-Thue systems.

Keywords

Characteristic Function Formal Power Series Independence Relation Finite Alphabet Commutative Monoid 
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 1988

Authors and Affiliations

  • Volker Diekert
    • 1
  1. 1.Institut für Informatik der Technischen Universität MünchenMünchen 2

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