On Hadamard Series and Rotating Q-Automata

Authors Louis-Marie Dando, Sylvain Lombardy

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Louis-Marie Dando
  • LaBRI UMR 5800, Université de Bordeaux, INP Bordeaux, CNRS, Bordeaux, FRANCE
Sylvain Lombardy
  • LaBRI UMR 5800, Université de Bordeaux, INP Bordeaux, CNRS, Bordeaux, FRANCE

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Louis-Marie Dando and Sylvain Lombardy. On Hadamard Series and Rotating Q-Automata. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


In this paper, we study rotating Q-automata, which are (memoryless) automata with weights in Q, that can read the input tape from left to right several times. We show that the series realized by valid rotating Q-automata are Q-Hadamard series (which are the closure of Q-rational series by pointwise inverse), and that every Q-Hadamard series can be realized by such an automaton. We prove that, although validity of rotating Q-automata is undecidable, the equivalence problem is decidable on rotating Q-automata. Finally, we prove that every valid two-way Q-automaton admits an equivalent rotating Q-automaton. The conversion, which is effective, implies the decidability of equivalence of two-way Q-automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Quantitative automata
  • Theory of computation → Algebraic language theory
  • Rational series
  • Hadamard operations
  • Rotating automata
  • Two-way automata


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