Abstract
The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendier in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation.
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References
P. Aczel. Non-Well-Founded Sets. CSLI Lecture Notes 14. Center for the Study of Languages and Information, Stanford, 1988.
P. Aczel and N. Mendier. A final coalgebra theorem. In D.H. Pitt et al., editors, Proc. Category Theory and Computer Science, pages 357–365. LNCS 389, 1989.
P. America and J.J.M.M. Rutten. Solving reflexive domain equations in a category of complete metric spaces. Journal of Computer Systems and Sciences, 39:343–375, 1989.
M. Barr. Terminal coalgebras in well-founded set theory. Theoretical Computer Science, 114:299–315, 1993. See also the addendum in Theoretical Computer Science, 124:189-192, 1994.
R. Blute, J. Desharnais, A. Edalat, and P. Panangaden. Bisimulation for labelled Markov processes. In Proc. LICS'97. Warzaw, 1997.
J.W. de Bakker and E.P. de Vink. Control Flow Semantics. The MIT Press, 1996.
A. Edalat. Domain theory and integration. In Proc. LICS'94, pages 115–124. Paris, 1994.
A. Giacalone, C. Jou, and S.A. Smolka. Algebraic reasoning for probabilisitic concurrent systems. In Proc. Working Conference on Programming Concepts and Methods. IFIP TC2, Sea of Gallilee, 1990.
R.J. van Glabbeek, S.A. Smolka, and B. Steffen. Reactive, generative and stratified models of probabilistic processes. Information and Computation, 121:59–80, 1995.
T.A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fülöp and F. Gécseg, editors, Proc. ICALP'95, pages 324–335. LNCS 944, 1995.
B. Jonsson and K.G-. Larsen. Specification and refinement of probabilistic processes. In Proc. LICS'91, pages 266–277. Amsterdam, 1991.
C. Jones and G. Plotkin. A probabilistic powerdomain of evaluations. In Proc. LICS'89, pages 186–195. Asilomar, 1989.
K.G. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94:1–28, 1991.
J.J.M.M. Rutten and D. Turi. On the foundations of final semantics: non-standard sets, metric spaces, partial orders. In J.W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proc. REX Workshop on Semantics: Foundations and Applications, pages 477–530. LNCS 666, 1993.
J.J.M.M. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In J.W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proc. REX School/Symposium ‘A Decade of Concurrency', pages 530–582. LNCS 803, 1994.
W. Rudin. Real and Complex Analysis. McGraw-Hill, 1966.
J.J.M.M. Rutten. Universal coalgebra: a theory of systems. Report CSR9652, CWI, 1996. Ftp-available at ftp.cwi.nl as pub/CWIreports/AP/CS-R9652.ps.Z.
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de Vink, E.P., Rutten, J.J.M.M. (1997). Bisimulation for probabilistic transition systems: A coalgebraic approach. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_202
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