Lower Bounds for Unambiguous Automata via Communication Complexity

Authors Mika Göös, Stefan Kiefer, Weiqiang Yuan

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Author Details

Mika Göös
  • EPFL, Lausanne, Switzerland
Stefan Kiefer
  • University of Oxford, UK
Weiqiang Yuan
  • EPFL, Lausanne, Switzerland


We thank anonymous ICALP reviewers for many comments.

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Mika Göös, Stefan Kiefer, and Weiqiang Yuan. Lower Bounds for Unambiguous Automata via Communication Complexity. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 126:1-126:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. 1) Complement: There is a language L recognised by an n-state UFA such that the complement language ̅L requires NFAs with n^Ω̃(log n) states. This improves on a lower bound by Raskin. 2) Union: There are languages L₁, L₂ recognised by n-state UFAs such that the union L₁∪L₂ requires UFAs with n^Ω̃(log n) states. 3) Separation: There is a language L such that both L and ̅L are recognised by n-state NFAs but such that L requires UFAs with n^Ω(log n) states. This refutes a conjecture by Colcombet.

Subject Classification

ACM Subject Classification
  • Theory of computation → Regular languages
  • Unambiguous automata
  • communication complexity


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