A Completeness Result for Finite λ-bisimulations

  • Joost Winter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9034)


We show that finite λ-bisimulations (closely related to bisimulations up to context) are sound and complete for finitely generated λ-bialgebras for distributive laws λ of a monad T on Set over an endofunctor F on Set, such that F preserves weak pullbacks and finitely generated T-algebras are closed under taking kernel pairs. This result is used to infer the decidability of weighted language equivalence when the underlying semiring is a subsemiring of an effectively presentable Noetherian semiring. These results are closely connected to [ÉM10] and [BMS13], concerned with respectively the decidability and axiomatization of weighted language equivalence w.r.t. Noetherian semirings.


Formal Power Series Completeness Result Forgetful Functor Algebra Morphism Coalgebra Structure 
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  1. 1.
    Adámek, J., Rosicky, J.: Locally Presentable and Accessible Categories. Cambridge University Press (1994)Google Scholar
  2. 2.
    Awodey, S.: Category Theory. Oxford University Press (2010)Google Scholar
  3. 3.
    Bartels, F.: On Generalized Coinduction and Probabilistic Specification Formats. PhD thesis, Vrije Universiteit Amsterdam (2004)Google Scholar
  4. 4.
    Bonchi, F., Bonsangue, M.M., Boreale, M., Rutten, J., Silva, A.: A coalgebraic perspective on linear weighted automata. Information and Computation 211, 77–105 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Bonsangue, M.M., Hansen, H.H., Kurz, A., Rot, J.: Presenting distributive laws. In: Heckel, R., Milius, S. (eds.) CALCO 2013. LNCS, vol. 8089, pp. 95–109. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  6. 6.
    Béal, M.-P., Lombardy, S., Sakarovitch, J.: Conjugacy and equivalence of weighted automata and functional transducers. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 58–69. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Bonsangue, M.M., Milius, S., Silva, A.: Sound and complete axiomatizations of coalgebraic language equivalence. ACM Transactions on Computational Logic 14(1), 7 (2013)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Borceux, F.: Handbook of Categorical Algebra. Basic category theory, vol. 1. Cambridge University Press (1994)Google Scholar
  9. 9.
    Bonchi, F., Pous, D.: Checking NFA equivalence with bisimulations up to congruence. In: POPL, pp. 457–468. ACM (2013)Google Scholar
  10. 10.
    Berstel, J., Reutenauer, C.: Noncommutative Rational Series with Applications. Cambridge University Press (2011)Google Scholar
  11. 11.
    Barr, M., Wells, C.: Toposes, triples and theories. Reprints in Theory and Applications of Categories 12, 1–287 (2006)Google Scholar
  12. 12.
    Caucal, D.: Graphes canoniques de graphes algébriques. ITA 24, 339–352 (1990)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Christensen, S., Hüttel, H., Stirling, C.: Bisimulation equivalence is decidable for all context-free processes. Information and Computation 121(2), 143–148 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Eilenberg, S.: Automata, Languages, and Machines. Academic Press, Inc. (1976)Google Scholar
  15. 15.
    Ésik, Z., Maletti, A.: Simulation vs. equivalence. In: Arabnia, H.R., Gravvanis, G.A., Solo, A.M.G. (eds.) FCS, pp. 119–124. CSREA Press (2010)Google Scholar
  16. 16.
    Heckel, R., Milius, S. (eds.): CALCO 2013. LNCS, vol. 8089. Springer, Heidelberg (2013)zbMATHGoogle Scholar
  17. 17.
    Jacobs, B.: A bialgebraic review of deterministic automata, regular expressions and languages. In: Futatsugi, K., Jouannaud, J.-P., Meseguer, J. (eds.)Goguen Festschr 2006. LNCS, vol. 4060, pp. 375–404. Springer, Heidelberg (2006)Google Scholar
  18. 18.
    Jacobs, B., Silva, A., Sokolova, A.: Trace semantics via determinization. In: Pattinson, D., Schröder, L. (eds.) CMCS 2012. LNCS, vol. 7399, pp. 109–129. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  19. 19.
    Klin, B.: Bialgebras for structural operational semantics: An introduction. Theoretical Computer Science 412(38), 5043–5069 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Lenisa, M.: From set-theoretic coinduction to coalgebraic coinduction: some results, some problems. Electronic Notes in Theoretical Computer Science 19, 2–22 (1999)CrossRefMathSciNetGoogle Scholar
  21. 21.
    MacLane, S.: Categories for the Working Mathematician. Graduate Texts in Mathematics, vol. 5. Springer, New York (1971)Google Scholar
  22. 22.
    Pous, D.: Coalgebraic up-to techniques. In: Heckel, R., Milius, S. (eds.) CALCO 2013. LNCS, vol. 8089, pp. 34–35. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  23. 23.
    Pous, D., Sangiorgi, D.: Enhancements of the coinductive proof method. In: Advanced Topics in Bisimulation and Coinduction. Cambridge University Press (2011)Google Scholar
  24. 24.
    Rot, J., Bonchi, F., Bonsangue, M.M., Pous, D., Rutten, J., Silva, A.: Enhanced coalgebraic bisimulation. Submitted to Mathematical Structures in Computer Science (2013)Google Scholar
  25. 25.
    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
  26. 26.
    Rutten, J.: Universal coalgebra: A theory of systems. Theoretical Computer Science 249(1), 3–80 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Silva, A., Bonchi, F., Bonsangue, M.M., Rutten, J.: Generalizing the powerset construction, coalgebraically. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS. LIPIcs, vol. 8, pp. 272–283. Schloss Dagstuhl—Leibniz-Zentrum für Informatik (2010)Google Scholar
  28. 28.
    Silva, A., Bonchi, F., Bonsangue, M., Rutten, J.: Generalizing determinization from automata to coalgebras. Logical Methods in Computer Science 9(1) (2013)Google Scholar
  29. 29.
    Schützenberger, M.-P.: On the definition of a family of automata. Information and Control 4(2-3), 245–270 (1961)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Winter, J., Bonsangue, M.M., Rutten, J.J.M.M.: Coalgebraic characterizations of context-free languages. Logical Methods in Computer Science 9(3:14) (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Joost Winter
    • 1
  1. 1.Faculty of Mathematics, Informatics, and MechanicsUniversity of WarsawWarsawPoland

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