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A Tropical Approach to the Compositional Piecewise Complexity of Words and Compressed Words

Authors Philippe Schnoebelen , J. Veron, Isa Vialard

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ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Tropical semiring
  • Subwords and subsequences
  • piecewise complexity
  • SLP-compressed words

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Abstract

We express the piecewise complexity of words using tools and concepts from tropical algebra. This allows us to define a notion of piecewise signature of a word that has size log(n)m^{O(1)} where m is the alphabet size and n is the length of the word. The piecewise signature of a concatenation can be computed from the signatures of its components, allowing a polynomial-time algorithm for computing the piecewise complexity of SLP-compressed words.

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Philippe Schnoebelen, J. Veron, and Isa Vialard. A Tropical Approach to the Compositional Piecewise Complexity of Words and Compressed Words. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 171:1-171:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.171

Author Details

Philippe Schnoebelen
  • Université Paris-Saclay, CNRS, ENS Paris-Saclay, Laboratoire Méthodes Formelles, Gif-sur-Yvette, France
J. Veron
  • Université Paris-Saclay, CNRS, ENS Paris-Saclay, Laboratoire Méthodes Formelles, Gif-sur-Yvette, France
Isa Vialard
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbrücken, Germany

Acknowledgements

Work started while the third author was at Univ. Paris-Saclay.

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