Critical Exponent of Infinite Balanced Words via the Pell Number System

  • Aseem R. BaranwalEmail author
  • Jeffrey Shallit
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11682)


In a recent paper of Rampersad et al., the authors conjectured that the smallest possible critical exponent of an infinite balanced word over a 5-letter alphabet is 3/2. We prove this result, using a formulation of first-order logic, the Pell number system, and a machine computation based on finite-state automata.


Critical exponent Balanced word Automatic theorem-proving 



We thank Narad Rampersad and Luke Schaeffer for their helpful comments. We are also grateful to the referees who read the paper and offered many useful suggestions.


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Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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