Abstract
Behavioural pseudometrics are a quantitative analogue of behavioural equivalences. They provide robust models for those concurrent systems in which quantitative data plays a crucial role. In this paper, we show how behavioural pseudometrics can be defined coalgebraically. Our results rely on the theory of accessible categories. We apply our results to obtain a robust model for probabilistic systems.
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
Adámek, J., Rosický, J.: Locally Presentable and Accessible Categories. Cambridge University Press, Cambridge (1994)
Arbib, M.A., Manes, E.G.: Arrows, Structures, and Functors: the categorical imperative. Academic Press, London (1975)
de Bakker, J.W., de Vink, E.P.: Control Flow Semantics. The MIT Press, Cambridge (1996)
Barr, M.: Terminal coalgebras in well-founded set theory. Theoretical Computer Science 114(2), 299–315 (1993)
Billingsley, P.: Probability and Measure. John Wiley & Sons, Chichester (1995)
van Breugel, F., Worrell, J.: Towards quantitative verification of probabilistic transition systems. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 421–432. Springer, Heidelberg (2001)
van Breugel, F., Worrell, J.: A behavioural pseudometric for metric labelled transition systems (2005)
van Breugel, F., Worrell, J.: A behavioural pseudometric for probabilistic transition systems. Theoretical Computer Science 331(1), 115–142 (2005)
de Alfaro, L.: Quantitative verification and control via the mu-calculus. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 102–126. Springer, Heidelberg (2003)
de Alfaro, L., Faella, M., Stoelinga, M.: Linear and branching metrics for quantitative transition systems. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 97–109. Springer, Heidelberg (2004)
de Alfaro, L., Henzinger, T.A., Majumdar, R.: Discounting the future in systems theory. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1022–1037. Springer, Heidelberg (2003)
Deng, Y., Chothia, T., Palamidessi, C., Pang, J.: Metrics for action-labelled quantitative transition systems. In: Proceedings of QAPL. ENTCS. Elsevier, Amsterdam (2005)
Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labeled Markov systems. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 258–273. Springer, Heidelberg (1999)
Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: The metric analogue of weak bisimulation for probabilistic processes. In: Proceedings of LICS, pp. 413–422. IEEE, Los Alamitos (2002)
Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labelled Markov processes. Theoretical Computer Science 318(3), 323–354 (2004)
Edgar, G.A.: Integral, Probability, and Fractal Measures. Springer, Heidelberg (1998)
Engelking, R.: General Topology. Heldermann Verlag (1989)
Giacalone, A., Jou, C.-C., Smolka, S.A.: Algebraic reasoning for probabilistic concurrent systems. In: Proceedings of PROCOMET, pp. 443–458. North-Holland, Amsterdam (1990)
Gupta, V., Jagadeesan, R., Panangaden, P.: Approximate reasoning for real-time probabilistic processes. In: Proceedings of QEST, pp. 304–313. IEEE, Los Alamitos (2004)
Heckmann, R.: Probabilistic domains. In: Tison, S. (ed.) CAAP 1994. LNCS, vol. 787, pp. 142–156. Springer, Heidelberg (1994)
Jacobs, B., Rutten, J.J.M.M.: A tutorial on (co)algebras and (co)induction. Bulletin of the EATCS 62, 222–259 (1997)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Information and Computation 94(1), 1–28 (1991)
Mac Lane, S.: Categories for the Working Mathematician. Springer, Heidelberg (1971)
Makkai, M., Paré, R.: Accessible Categories: The Foundation of Categorical Model Theory. American Mathematical Society, Providence (1989)
Parthasarathy, K.R.: Probability Measures on Metric Spaces. Academic Press, London (1967)
Turi, D., Rutten, J.J.M.M.: On the foundations of final coalgebra semantics: non-well-founded sets, partial orders, metric spaces. Mathematical Structures in Computer Science 8(5), 481–540 (1998)
de Vink, E.P., Rutten, J.J.M.M.: Bisimulation for probabilistic transition systems: a coalgebraic approach. Theoretical Computer Science 221(1/2), 271–293 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
van Breugel, F., Hermida, C., Makkai, M., Worrell, J. (2005). An Accessible Approach to Behavioural Pseudometrics. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_82
Download citation
DOI: https://doi.org/10.1007/11523468_82
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27580-0
Online ISBN: 978-3-540-31691-6
eBook Packages: Computer ScienceComputer Science (R0)