Abstract
Coalgebra offers a general framework for modelling different types of state-based systems. Our aim is to present generic algorithms to decide behavioural equivalence for coalgebras which generalize partition refinement. The underlying idea of the algorithms is to work on the final chain and to factor out redundant information. If the algorithm terminates, the result of the construction is a representative of the given coalgebra that is not necessarily unique and that allows to precisely answer questions about behavioural equivalence. We apply the algorithm to weighted automata over semirings in order to obtain a procedure for checking language equivalence for a large number of semirings.
Chapter PDF
Similar content being viewed by others
Keywords
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
Adámek, J., Bonchi, F., Hülsbusch, M., König, B., Milius, S., Silva, A.: A coalgebraic perspective on minimization and determinization. In: Birkedal, L. (ed.) FOSSACS 2012. LNCS, vol. 7213, pp. 58–73. Springer, Heidelberg (2012)
Almagor, S., Boker, U., Kupferman, O.: What’s decidable about weighted automata? In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 482–491. Springer, Heidelberg (2011)
Adámek, J., Herrlich, H., Strecker, G.E.: Abstract and Concrete Categories - The Joy of Cats. Wiley (1990)
Adámek, J., Koubek, V.: On the greatest fixed point of a set functor. Theoretical Computer Science 150, 57–75 (1995)
Adámek, J., Rosický, J.: Locally Presentable and Accessible Categories. London Mathematical Society Lecture Note Series, vol. 189. Cambridge University Press (1994)
Baier, C.: Polynomial time algorithms for testing probabilistic bisimulation and simulation. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 50–61. Springer, Heidelberg (1996)
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)
Bonsangue, M., Milius, S., Silva, A.: Sound and complete axiomatizations of coalgebraic language equivalence. ACM Transactions on Computational Logic 14(1) (2013)
Boreale, M.: Weighted bisimulation in linear algebraic form. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 163–177. Springer, Heidelberg (2009)
Bonchi, F., Petrisan, D., Pous, D., Rot, J.: Coinduction up to in a fibrational setting. CoRR abs/1401.6675 (2014)
Berstel, J., Reutenauer, C.: Rational Series and their Languages. Springer (1988)
Droste, M., Kuske, D.: Weighted automata. To appear in Automata: from Mathematics to Applications. European Mathematical Society (2013)
Droste, M., Werner, K., Vogler, H.: Handbook of Weighted Automata. Springer (2009)
Mohri, M.: Weighted automata algorithms. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, pp. 213–254. Springer (2009)
Ésik, Z., Maletti, A.: Simulation vs. equivalence. In: Proc. of FCS 2010, pp. 119–124 (2010)
Ferrari, G., Montanari, U., Tuosto, E.: Coalgebraic minimization of HD-automata for the π-calculus using polymorphic types. Theor. Comput. Sci. 331(2-3), 325–365 (2005)
Hasuo, I., Jacobs, B., Sokolova, A.: Generic trace semantics via coinduction. Logical Methods in Computer Science 3(4:11), 1–36 (2007)
Hopcroft, J.E., Ullman, J.D.: Introduction to automata theory, languages and computation. Addison Wesley, Reading (1979)
Kiefer, S., Murawski, A.S., Ouaknine, J., Wachter, B., Worrell, J.: Language equivalence for probabilistic automata. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 526–540. Springer, Heidelberg (2011)
Krob, D.: The equality problem for rational series with multiplicities in the tropical semiring is undecidable. In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 101–112. Springer, Heidelberg (1992)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing (preliminary report). In: Proc. of POPL 1989, pp. 344–352. ACM (1989)
Mohri, M.: Finite-state transducers in language and speech processing. Computational Linguistics 23, 269–311 (1997)
Mohri, M.: Weighted automata algorithms. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, pp. 213–254. Springer (2009)
Rot, J., Bonchi, F., Bonsangue, M., Rutten, J., Pous, D., Silva, A.: Enhanced coalgebraic bisimulation. In: Mathematical Structures in Computer Science (to appear, 2014)
Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theoretical Computer Science 249, 3–80 (2000)
Staton, S.: Relating coalgebraic notions of bisimulation. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 191–205. Springer, Heidelberg (2009)
Urabe, N., Hasuo, I.: Generic forward and backward simulations III: Quantitative simulations by matrices. In: Proc. of CONCUR 2014. LNCS/ARCoSS. Springer (to appear, 2014)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 IFIP International Federation for Information Processing
About this paper
Cite this paper
König, B., Küpper, S. (2014). Generic Partition Refinement Algorithms for Coalgebras and an Instantiation to Weighted Automata. In: Diaz, J., Lanese, I., Sangiorgi, D. (eds) Theoretical Computer Science. TCS 2014. Lecture Notes in Computer Science, vol 8705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44602-7_24
Download citation
DOI: https://doi.org/10.1007/978-3-662-44602-7_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44601-0
Online ISBN: 978-3-662-44602-7
eBook Packages: Computer ScienceComputer Science (R0)