The Language of Self-Avoiding Walks

Christian Lindorfer*, Wolfgang Woess

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let X = (VX, EX) be an infinite, locally finite, connected graph without loops or multiple edges. We consider the edges to be oriented, and EX is equipped with an involution which inverts the orientation. Each oriented edge is labelled by an element of a finite alphabet Σ. The labelling is assumed to be deterministic: edges with the same initial (resp. terminal) vertex have distinct labels. Furthermore, it is assumed that the group of label-preserving automorphisms of X acts quasi-transitively. For any vertex o of X, consider the language of all words over Σ which can be read along self-avoiding walks starting at o. We characterize under which conditions on the graph structure this language is regular or context-free. This is the case if and only if the graph has more than one end, and the size of all ends is 1, or at most 2, respectively.

Original languageEnglish
Pages (from-to)691-720
Number of pages30
Issue number5
Early online date2020
Publication statusPublished - Nov 2020

ASJC Scopus subject areas

  • Computational Mathematics
  • Discrete Mathematics and Combinatorics

Fields of Expertise

  • Information, Communication & Computing


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