Optimal Regular Expressions for Permutations (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors Antonio Molina Lovett , Jeffrey Shallit

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Antonio Molina Lovett
  • University of Waterloo, Canada
Jeffrey Shallit
  • University of Waterloo, Canada

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Antonio Molina Lovett and Jeffrey Shallit. Optimal Regular Expressions for Permutations (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 121:1-121:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


The permutation language P_n consists of all words that are permutations of a fixed alphabet of size n. Using divide-and-conquer, we construct a regular expression R_n that specifies P_n. We then give explicit bounds for the length of R_n, which we find to be 4^{n}n^{-(lg n)/4+Theta(1)}, and use these bounds to show that R_n has minimum size over all regular expressions specifying P_n.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • regular expressions
  • lower bounds
  • divide-and-conquer


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