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Commutative ℕ-Rational Series of Polynomial Growth

Author Aliaume Lopez

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ACM Subject Classification
  • Theory of computation → Quantitative automata
  • Theory of computation → Transducers
Keywords
  • Rational series
  • weighted automata
  • polyregular function
  • commutative

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Abstract

This paper studies which functions computed by ℤ-weighted automata can be realised by ℕ-weighted automata, under two extra assumptions: commutativity (the order of letters in the input does not matter) and polynomial growth (the output of the function is bounded by a polynomial in the size of the input). We leverage this effective characterization to decide whether a function computed by a commutative ℕ-weighted automaton of polynomial growth is star-free, a notion borrowed from the theory of regular languages that has been the subject of many investigations in the context of string-to-string functions during the last decade.

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Aliaume Lopez. Commutative ℕ-Rational Series of Polynomial Growth. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 67:1-67:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.67

Author Details

Aliaume Lopez
  • University of Warsaw, Poland

Funding

Aliaume Lopez was supported by the Polish National Science Centre (NCN) grant "Polynomial finite state computation" (2022/46/A/ST6/00072).

References

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