Functional Closure Properties of Finite ℕ-Weighted Automata

Authors Julian Dörfler , Christian Ikenmeyer

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Julian Dörfler
  • Saarland Informatics Campus (SIC), Saarbrücken Graduate School of Computer Science, Saarland University, Germany
Christian Ikenmeyer
  • University of Warwick, Coventry, UK

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Julian Dörfler and Christian Ikenmeyer. Functional Closure Properties of Finite ℕ-Weighted Automata. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 134:1-134:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


We determine all functional closure properties of finite ℕ-weighted automata, even all multivariate ones, and in particular all multivariate polynomials. We also determine all univariate closure properties in the promise setting, and all multivariate closure properties under certain assumptions on the promise, in particular we determine all multivariate closure properties where the output vector lies on a monotone algebraic graph variety.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata extensions
  • Finite automata
  • weighted automata
  • counting
  • closure properties
  • algebraic varieties


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