A Normalized Edit Distance on Infinite Words

Authors Dana Fisman , Joshua Grogin , Gera Weiss

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Author Details

Dana Fisman
  • Dept. of Computer Science, Ben-Gurion University, Beer-Sheva, Israel
Joshua Grogin
  • Dept. of Computer Science, Ben-Gurion University, Beer-Sheva, Israel
Gera Weiss
  • Dept. of Computer Science, Ben-Gurion University, Beer-Sheva, Israel

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Dana Fisman, Joshua Grogin, and Gera Weiss. A Normalized Edit Distance on Infinite Words. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We introduce ω^ ̅-NED, an edit distance between infinite words, that is a natural extension of NED, the normalized edit distance between finite words. We show it is a metric on (equivalence classes of) infinite words. We provide a polynomial time algorithm to compute the distance between two ultimately periodic words, and a polynomial time algorithm to compute the distance between two regular ω-languages given by non-deterministic Büchi automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Pattern matching
  • Hardware → Robustness
  • Edit Distance
  • Infinite Words
  • Robustness


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