Coalgebraic Semantics of Heavy-Weighted Automata

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9463)

Abstract

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.

References

  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)MathSciNetCrossRefMATHGoogle 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)CrossRefMATHGoogle 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)MATHGoogle 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). http://oai.cwi.nl/oai/asset/22603/22603D.pdf
  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)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Rutten, J.J.M.M.: Coinductive counting with weighted automata. J. Automata Lang. Comb. 8(2), 319–352 (2003)MathSciNetMATHGoogle Scholar
  11. 11.
    Rutten, J.J.M.M.: A coinductive calculus of streams. Math. Struct. Comput. Sci. 15(1), 93–147 (2005)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press, New York (2009)CrossRefMATHGoogle 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)MATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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