Coalgebraic Semantics of Heavy-Weighted Automata

  • Marie Fortin
  • Marcello M. Bonsangue
  • Jan Rutten
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9463)


In this paper we study heavy-weighted automata, a generalization of weighted automata in which the weights of the transitions can be formal power series. As for ordinary weighted automata, the behaviour of heavy-weighted automata is expressed in terms of formal power series. We propose several equivalent definitions for their semantics, including a system of behavioural differential equations (following the approach of coinductive calculus), or an embedding into a coalgebra for the functor \(S\,\times \,(-)^A\), for which the set of formal power series is a final coalgebra. Using techniques based on bisimulations and coinductive calculus, we study how ordinary weighted automata can be transformed into more compact heavy-weighted ones.


  1. 1.
    Bonchi, F., Bonsangue, M.M., Boreale, M., Rutten, J.J.M.M., Silva, A.: A coalgebraic perspective on linear weighted automata. Inf. Comput. 211, 77–105 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bonsangue, M.M., Rutten, J., Winter, J.: Defining context-free power series coalgebraically. In: Pattinson, D., Schröder, L. (eds.) CMCS 2012. LNCS, vol. 7399, pp. 20–39. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Brzozowski, J., Mccluskey, E.J.: Signal flow graph techniques for sequential circuit state diagrams. IEEE Trans. Electron. Comput. 12(2), 67–76 (1963)CrossRefGoogle Scholar
  4. 4.
    Castro, R.D., Ramírez, A., Ramírez, J.L.: Applications in enumerative combinatorics of infinite weighted automata and graphs. Sci. Annal. Comput. Sci. 24(1), 137–171 (2014)MathSciNetGoogle Scholar
  5. 5.
    Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata. Monographs in Theoretical Computer Science. An EATCS Series, 1st edn. Springer, Heidelberg (2009)zbMATHGoogle Scholar
  6. 6.
    Fortin, M., Bonsangue, M.M., Rutten, J.J.M.M.: Coalgebraic semantics of heavy-weighted automata. Technical report FM-1405, CWI - Amsterdam (2014).
  7. 7.
    Petre, I., Salomaa, A.: Algebraic systems and pushdown automata. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata [5]. Monographs in Theoretical Computer Science. An EATCS Series, pp. 257–289. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Rot, J., Bonsangue, M., Rutten, J.: Coalgebraic bisimulation-up-to. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds.) SOFSEM 2013. LNCS, vol. 7741, pp. 369–381. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Rutten, J.J.M.M.: Behavioural differential equations: a coinductive calculus of streams, automata, and power series. Theoret. Comput. Sci. 308(1–3), 1–53 (2003)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Rutten, J.J.M.M.: Coinductive counting with weighted automata. J. Automata Lang. Comb. 8(2), 319–352 (2003)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Rutten, J.J.M.M.: A coinductive calculus of streams. Math. Struct. Comput. Sci. 15(1), 93–147 (2005)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press, New York (2009)CrossRefGoogle Scholar
  13. 13.
    Silva, A., Bonchi, F., Bonsangue, M.M., Rutten, J.J.M.M.: Generalizing determinization from automata to coalgebras. Log. Methods Comput. Sci. 9(1) (2013)Google Scholar
  14. 14.
    Wood, D.: Theory of Computation. Harper & Row, New York (1987)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marie Fortin
    • 1
    • 3
  • Marcello M. Bonsangue
    • 2
    • 3
  • Jan Rutten
    • 3
    • 4
  1. 1.École Normale Supérieure de CachanCachanFrance
  2. 2.LIACS – Leiden UniversityLeidenThe Netherlands
  3. 3.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands
  4. 4.ICIS – Radboud University NijmegenNijmegenThe Netherlands

Personalised recommendations