On two-sided infinite fixed points of morphisms

  • Authors:
  • Jeffrey Shallit;Ming-wei Wang

  • Affiliations:
  • Univ. of Waterloo, Ontario, Canada;Univ. of Waterloo, Ontario, Canada

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2002

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Abstract

Let &Sgr; be a finite alphabet, and let h:&Sgr;*&Sgr; be a morphism. Finite and infinite fixed points of morphismsi.e., those words w such that h(w)=wplay an important role in formal language theory. Head characterized the finite fixed points of h, and later, Head and Lando characterized the one-sided infinite fixed points of h. Our paper has two main results. First, we complete the characterization of fixed points of morphisms by describing all two-sided infinite fixed points of h, for both the "pointed" and "unpointed" cases. Second, we completely characterize the solutions to the equation h(xy)=yx in finite words.