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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)
https://doi.org/10.4230/LIPIcs.MFCS.2018.6

Abstract

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
Keywords
  • Rational series
  • Hadamard operations
  • Rotating automata
  • Two-way automata

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References

  1. Marcella Anselmo and Alberto Bertoni. Two-way probabilistic automata and rational power series. In Proc. IV Conv. It. Inform. Teor., pages 9-23. World Scientific, 1992. Google Scholar
  2. Jean Berstel and Christophe Reutenauer. Noncommutative Rational Series with Applications, volume 137 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 2010. Google Scholar
  3. John H. Conway. Regular Algebra and Finite Machines. Chapman and Hall, London, 1971. Google Scholar
  4. Louis-Marie Dando and Sylvain Lombardy. From Hadamard Expressions to Weighted Rotating Automata and Back. In CIAA'17, volume 10328 of LNCS, pages 163-174. Springer, 2017. URL: http://dx.doi.org/10.1007/978-3-319-60134-2_14.
  5. Zoltán Ésik and Werner Kuich. Rationally additive semirings. J. UCS, 8(2):173-183, 2002. URL: http://dx.doi.org/10.3217/jucs-008-02-0173.
  6. Michel Fliess. Matrices de Hankel. J. Math. Pures et Appl., 53:197-222, 1974. Google Scholar
  7. Bruno Guillon. Input- or output-unary sweeping transducers are weaker than their 2-way counterparts. RAIRO - Theor. Inf. and Applic., 50(4):275-294, 2016. URL: http://dx.doi.org/10.1051/ita/2016028.
  8. Christos Kapoutsis, Richard Královič, and Tobias Mömke. Size complexity of rotating and sweeping automata. Journal of Computer and System Sciences, 78(2):537-558, 2012. URL: http://dx.doi.org/10.1016/j.jcss.2011.06.004.
  9. Sylvain Lombardy. Two-way representations and weighted automata. RAIRO - Theoretical Informatics and Applications, 50(4):331-350, 2016. URL: http://dx.doi.org/10.1051/ita/2016026.
  10. Azaria Paz. Introduction to Probabilistic Automata (Computer Science and Applied Mathematics). Academic Press, Inc., Orlando, FL, USA, 1971. Google Scholar
  11. Giovanni Pighizzini. Two-way finite automata: Old and recent results. Fundam. Inform., 126(2-3):225-246, 2013. URL: http://dx.doi.org/10.3233/FI-2013-879.
  12. Christophe Reutenauer. Sur les éléments inversibles de l'algèbre de Hadamard des séries rationnelles. Bull. Soc. Math. France, 110:225-232, 1982. Google Scholar
  13. Jacques Sakarovitch. Elements of Automata Theory. Cambridge University Press, 2009. Google Scholar
  14. Davod Khojasteh Salkuyeh. Comments on "a note on a three-term recurrence for a tridiagonal matrix". Appl. Math. Comput., 176(2):442-444, 2006. URL: http://dx.doi.org/10.1016/j.amc.2005.09.033.
  15. Marcel-Paul Schützenberger. On the definition of a family of automata. Inform. and Control, 4:245-270, 1961. URL: http://dx.doi.org/10.1016/S0019-9958(61)80020-X.
  16. Marcel-Paul Schützenberger. On a theorem of R. Jungen. Proc. Amer. Math. Soc., 13(6):885-890, 1962. Google Scholar
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