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Defining Context-Free Power Series Coalgebraically

  • Marcello M. Bonsangue
  • Jan Rutten
  • Joost Winter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7399)

Abstract

In this paper we present a coinductive definition of context free power series in terms of behavioural differential equations. We show that our coalgebraic approach provides a unified view on many, at first sight different, existing notions of algebraicity, and we apply our behavioural differential equations to produce a new proof for a classical result by Chomsky and Schützenberger, and a simple proof that the zip-operator of two algebraic streams is algebraic.

Keywords

Normal Form Power Series Strong Solution Formal Power Series Disjunctive Normal Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [AS03]
    Allouche, J.-P., Shallit, J.O.: Automatic Sequences – Theory, Applications, Generalizations. Cambridge University Press (2003)Google Scholar
  2. [BR11]
    Berstel, J., Reutenauer, C.: Noncommutative Rational Series with Applications. Cambridge University Press (2011)Google Scholar
  3. [ÉL05]
    Ésik, Z., Leiß, H.: Algebraically complete semirings and Greibach normal form. Annals of Pure and Applied Logic 133(1-3), 173–203 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  4. [Fli74]
    Fliess, M.: Sur divers produits de sries formelles. Bulletin de la S.M.F. 102, 181–191 (1974)MathSciNetzbMATHGoogle Scholar
  5. [Nij80]
    Nijholt, A.: Context-Free Grammars: Covers, Normal Forms, and Parsing. LNCS, vol. 93. Springer, Heidelberg (1980)zbMATHCrossRefGoogle Scholar
  6. [NR10]
    Niqui, M., Rutten, J.: Sampling, Splitting and Merging in Coinductive Stream Calculus. In: Bolduc, C., Desharnais, J., Ktari, B. (eds.) MPC 2010. LNCS, vol. 6120, pp. 310–330. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. [PS09]
    Petre, I., Salomaa, A.: Algebraic systems and pushdown automata. In: Handbook of Weighted Automata, 1st edn., pp. 257–289. Springer (2009)Google Scholar
  8. [Rut02]
    Rutten, J.: Coinductive counting: bisimulation in enumerative combinatorics. Electr. Notes Theor. Comput. Sci. 65(1), 286–304 (2002)CrossRefGoogle Scholar
  9. [Rut03]
    Rutten, J.: Behavioural differential equations: a coinductive calculus of streams, automata, and power series. Theoretical Computer Science 308(1-3), 1–53 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  10. [Rut05]
    Rutten, J.: A coinductive calculus of streams. Mathematical Structures in Computer Science 15(1), 93–147 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  11. [WBR11]
    Winter, J., Bonsangue, M.M., Rutten, J.: Context-Free Languages, Coalgebraically. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 359–376. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. [SBBR10]
    Silva, A., Bonchi, F., Bonsangue, M., Rutten, J.: Generalizing the powerset construction, coalgebraically. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2010. LIPIcs, vol. 8, pp. 272–283 (2010)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2012

Authors and Affiliations

  • Marcello M. Bonsangue
    • 2
    • 1
  • Jan Rutten
    • 1
    • 3
  • Joost Winter
    • 1
  1. 1.Centrum Wiskunde & Informatica (CWI)The Netherlands
  2. 2.LIACSLeiden UniversityThe Netherlands
  3. 3.Radboud UniversityNijmegenThe Netherlands

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