Abstract
The existence of bisimulations for objects in the Kleisli category associated with the Giry monad of subprobabilities over Polish spaces is studied. We first investigate these morphisms and show that the problem can be reduced to the existence of bisimulations for objects in the base category of stochastic relations using simulation equivalent congruences. This leads to a criterion for two objects related through the monad to be bisimilar.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramsky, S., Blute, R., Panangaden, P.: Nuclear and trace ideal in tensored *-categories. J. Pure Appl. Alg. 143(1–3), 3–47 (1999)
Doberkat, E.-E.: Pipelines: Modelling a software architecture through relations. Acta Informatica 40, 37–79 (2003)
Doberkat, E.-E.: Eilenberg-Moore algebras for stochastic relations. Information and Computation 204, 1756–1781 (2006)
Doberkat, E.-E.: Stochastic relations: congruences, bisimulations and the Hennessy-Milner theorem. SIAM J. Computing 35(3), 590–626 (2006)
Doberkat, E.-E.: Kleisli morphisms and randomized congruences for the Giry monad. J. Pure Appl. Alg. 211, 638–664 (2007)
Doberkat, E.-E.: Stochastic Relations. Foundations for Markov Transition Systems. Chapman & Hall/CRC Press, Boca Raton, New York (2007)
Doberkat, E.-E., Schubert, C.: Coalgebraic logic for stochastic right coalgebras. Technical report, Chair for Software-Technology, University of Dortmund (September 2007)
Giry, M.: A categorical approach to probability theory. In: Categorical Aspects of Topology and Analysis, J. Pure Appl. Alg., 915, 68–85. (1981)
Mac Lane, S.: Categories for the Working Mathematician. In: Graduate Texts in Mathematics, Springer, Berlin (1997)
Moggi, E.: Notions of computation and monads. Information and Computation 93, 55–92 (1991)
Panangaden, P.: Probabilistic relations. In: Baier, C., Huth, M., Kwiatkowska, M., Ryan, M. (eds.) Proc. PROBMIV, pp. 59–74 (1998)
Parthasarathy, K.R.: Probability Measures on Metric Spaces. Academic Press, New York (1967)
Schröder, L., Pattinson, D.: Modular Algorithms for Heterogeneous Modal Logics. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 459–471. Springer, Heidelberg (2007)
Srivastava, S.M.: A Course on Borel Sets. In: Graduate Texts in Mathematics, Springer, Berlin (1998)
Zhou, C.: Complete Deductive Systems for Probabilistic Logic with Application to Harsany Type spaces. PhD thesis, Department of Mathematics, University of Indiana (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Doberkat, EE. (2008). Weak Bisimulations for the Giry Monad (Extended Abstract). In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2008. Lecture Notes in Computer Science, vol 4978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79228-4_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-79228-4_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79227-7
Online ISBN: 978-3-540-79228-4
eBook Packages: Computer ScienceComputer Science (R0)