Approximating labelled Markov processes

Information and Computation

Volumn 184, Issue 1, 2003, Pages 160-200

  Desharnais, Josée ^a   Gupta, Vineet ^b   Jagadeesan, Radha ^c   Panangaden, Prakash ^d  

^a UNIVERSITÉ LAVAL   (Canada)

^b GOOGLE INC   (United States)

^c DEPAUL UNIVERSITY   (United States)

^d MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; EQUIVALENCE CLASSES; FORMAL LOGIC; INTEGRAL EQUATIONS; PROBABILITY DISTRIBUTIONS; STATE SPACE METHODS; THEOREM PROVING;

FINITE MODEL THEOREM; LABELLED MARKOV PROCESSES; LABELLED TRANSITION SYSTEMS;

MARKOV PROCESSES;

EID: 0038804142     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0890-5401(03)00051-8     Document Type: Article

References (60)

1. S. Abramsky, A domain equation for bisimulation, Information Computation 92 (2) (1991) 161-218.
2. R. Alur, D. Dill, A theory of timed automata, Theoretical Computer Science 126 (1994) 183-235.
3. M. Alvarez-Manilla, A. Edalat, N. Saheb-Djahromi, An extension result for continuous valuations. Electronic Notes in Theoretical Computer Science 13 (1998).
4. A. Aziz, V. Singhal, F. Balarin, R.K. Brayton, A.L. Sangiovanni-Vincentelli, It usually works: the temporal logic of stochastic systems, in: Proceedings of the Conference on Computer-Aided Verification, 1995.
5. J.C.M. Baeten, J.A. Bergstra, S.A. Smolka, Axiomatizing probabilistic processes: ACP with generative probabilities, Information and Computation 121 (2) (1995) 234-255.
6. C. Baier, Ed Clark, V. Hartonas-Garmhausen, M. Kwiatkowska, M. Ryan, Symbolic model checking for probabilistic processes, in: Proceedings of the 24th International Colloquium On Automata Languages And Programming, vol. 1256, Lecture Notes In Computer Science, 1997, pp. 430-440.
7. A. Bianco, L. de Alfaro, Model checking of probabilistic and nondeterministic systems, in: P.S. Thiagarajan (Ed.), Proceedings of the 15th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, vol. 1026, Lecture Notes In Computer Science, 1995, pp. 499-513.
8. R. Blute, J. Desharnais, A. Edalat, P. Panangaden, Bisimulation for labelled Markov processes, in: Proceedings of the Twelfth IEEE Symposium On Logic In Computer Science, Warsaw, Poland, 1997.
9. C. Baier, M. Kwiatkowska, Domain equations for probabilistic processes. Available from URL (http://www.cs.bham.ac.uk/mzk/), March 1996.
10. C. Baier, J.-P. Katonen, H. Hermans, Approximative symbolic model checking of continuous-time Markov chains, in: J.C.M. Baeten, S. Mauw (Eds.), Lecture Notes In Computer Science, vol. 1664, Springer, Berlin, 1999, pp. 146-161.
11. J. Bengtsson, K.G. Larsen, F. Larsson, P. Pettersson, W. Yi, UppAal: A tool suite for automatic verification of real-time systems, in: R. Alur, T. Henzinger, E. Sontag (Eds.), Hybrid Systems III, vol. 1066, Lecture Notes In Computer Science. 1996, pp. 232-243.
12. R. Cleaveland, Fully abstract characterizations of testing preorders for probabilistic processes, in: CONCUR 94, Lecture Notes in Computer Science, vol. 836, Springer, Berlin, 1994, pp. 497-512.
13. R. Cleaveland, S. Smolka, A. Zwarico, Testing preorders for probabilistic processes, in: W. Kuich (Ed.), Lecture Notes in Computer Science, vol. 623, Springer, Berlin, 1992, pp. 708-719.
14. C. Courcoubetis, M. Yannakakis, The complexity of probabilistic verification, Journal of the ACM 42 (4) (1995) 857-907.
15. J. Desharnais, A. Edalat, P. Panangaden, A logical characterization of bisimulation for labeled Markov processes, in: Proceedings of the 13th IEEE Symposium On Logic In Computer Science, Indianapolis, IEEE Press, Indianapolis, 1998, pp. 478-489.
16. J. Desharnais, A. Edalat, P. Panangaden, Bisimulation for labeled Markov processes, Information and Computation (2002).
17. J. Desharnais, Logical characterization of simulation for Markov chains, in: M. Kwiatkowska (Ed.), Probmiv99, Proceedings of the Second International Workshop on Probabilistic Methods in Verification, The University of Birmingham, 1999, pp. 33-48.
18. J. Desharnais, V. Gupta, R. Jagadeesan, P. Panangaden, Metrics for labeled Markov systems (Available as TR: CSR-99-8). in: Proceedings of CONCUR99, Lecture Notes in Computer Science, Springer, Berlin, 1999.
19. J. Desharnais, V. Gupta, R. Jagadeesan, P. Panangaden, Approximation of labeled markov processes, in: Proceedings of the Fifteenth Annual IEEE Symposium On Logic In Computer Science, IEEE Computer Society Press, 2000, pp. 95-106.
20. E. de Vink, J.J.M.M. Rutten, Bisimulation for probabilistic transition systems: A coalgebraic approach, in: Proceedings of the 24th International Colloquium On Automata Languages And Programming, 1997.
21. A. Edalat, Domain of computation of a random field in statistical physics, in: C. Hankin, I. Mackie, R. Nagarajan (Eds.), Theory and Formal Methods 1994: Proceedings of the second Imperial College Department of Computing Workshop on Theory and Formal Methods, IC Press, 1994, pp. 11-14.
22. A. Edalat, Domain theory and integration, Theoretical Computer Science 151 (1995) 163-193.
23. A. Edalat, Domain theory in stochastic processes, Proceedings of the Tenth Annual IEEE Symposium On Logic In Computer Science, IEEE Computer Society Press, 1995.
24. A. Edalat, Dynamical systems, measures and fractals via domain theory, Information and Computation 120 (1) (1995) 32-48.
25. A. Einstein, The theory of the brownian movement, Annalen der Physik 17 (1905) 549.
26. W. Feller, An Introduction to Probability Theory and its Applications II, second ed., Wiley, 1971.
27. M. Giry, A categorical approach to probability theory, in: B. Banaschewski (Ed.), Lecture Notes In Mathematics, vol. 915, Springer, Berlin, 1981, pp. 68-85.
28. V. Gupta, R. Jagadeesan, P. Panangaden, Stochastic processes as concurrent constraint programs, in: Proceedings of the 26th Proceedings of the Annual ACM symposium on Principles of Programming Languages, 1999.
29. H.A. Hansson, Real-time Safety-critical Systems, Elsevier, Amsterdam, 1994.
30. T. Henzinger, P.-H. Ho, H. Wong-Toi, Hytech: a model checker for hybrid systems, Software Tools for Technology Transfer 1 (1) (1997) 110-122.
31. J. Hillston, A compositional approach to performance modelling, Ph.D. thesis, University of Edinburgh, 1994. Published as a Distinguished Dissertation by Cambridge University Press in 1996.
32. H. Hansson, B. Jonsson, A logic for reasoning about time and reliability, Formal Aspects of Computing 6 (5) (1994) 512-535.
33. M. Huth, M. Kwiatkowska, Quantitative analysis and model checking, Proceedings of the 12th IEEE Symposium on Logic in Computer Science, IEEE Press, 1997, pp. 111-122.
34. S. Hart, M. Sharir, Probabilistic propositional temporal logics, Information and Control 70 (1986) 97-155.
35. B. Jonsson, K. Larsen, Specification and refinement of probabilistic processes, in: Proceedings of the 6th Annual IEEE Symposium on Logic in Computer Science, 1991.
36. C. Jones, Probabilistic Non-determinism, Ph.D. thesis, University of Edinburgh, 1990. CST-63-90.
37. C. Jones, G.D. Plotkin, A probabilistic powerdomain of evaluations, in: Proceedings of the Fourth Annual IEEE Symposium on Logic in Computer Science, 1989, pp. 186-195.
38. A. Jung, R. Tix, The troublesome probabilistic powerdomain. Electronic Notes in Theoretical Computer Science 13 (1998).
39. A. Jung, Cartesian closed categories of domains, Ph.D. thesis, Technischen Hogschule Darmstadt, 1988.
40. B. Jonsson, W. Yi, Compositional testing preorders for probabilistic processes, in: Proceedings of the 10th Annual IEEE Symposium On Logic In Computer Science, 1995, pp. 431-441.
41. D. Kozen, Semantics of probabilistic programs, Journal of Computer and Systems Sciences 22 (1981) 328-350.
42. D. Kozen, A probabilistic PDL, Journal of Computer and Systems Sciences 30 (2) (1985) 162-178.
43. J.G. Kemeny, J.L. Snell, Finite Markov Chains, Van Nostrand, 1960.
44. J.D. Lawson, Valuations on continuous lattices, in: R.-E. Hoffman (Ed.), Mathematik Arbeitspapiere, vol. 27, Universität Bremen, 1982, pp. 204-225.
45. J. Lawson, Spaces of maximal points, Mathematical Structures in Computer Science 7 (5) (1997) 543-555.
46. K.G. Larsen, A. Skou, Bisimulation through probablistic testing. Information and Computation 94 (1999) 1-28.
47. M. Ajmone Marsan, Stochastic petri nets: an elementary introduction, in: Advances in Petri Nets 1989, Springer, Berlin, 1989, pp. 1-29.
48. R. Milner, Communication and Concurrency, Prentice-Hall, New York, 1989.
49. B. Øksendal, Stochastic Differential Equations, Springer, Berlin, 1995.
50. P. Panangaden, Probabilistic relations, in: C. Baier, M. Huth, M. Kwiatkowska, M. Ryan (Eds.), PROBMIV98, 1998, pp. 59-74.
51. K.R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967.
52. N. Saheb-Djahromi, Probabilistic LCF, Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, vol. 64, Springer, Berlin, 1978.
53. N. Saheb-Djahromi, Cpos of measures for nondeterminism, Theoretical Computer Science 12 (1) (1980) 19-37.
54. R. Segala, Modeling and verification of randomized distributed real-time systems, Ph.D. thesis, MIT, Department of Electrical Engineering and Computer Science, 1995. Also appears as technical report MIT/LCS/TR-676.
55. M. Smoluchowski, Brownian motion, Annalen der Physik 21 (1906) 756.
56. M.B. Smyth, G.D. Plotkin, The category theoretic solution of recursive domain equations, SIAM Journal of Computing 11 (4) (1982).
57. F. van Breugel, J. Worrell, Towards quantitative verification of probabilistic systems, Proceedings of the Twenty-eighth International Colloquium on Automata, Languages and Programming, Springer, Berlin, 2001.
58. R. van Glabbeek, S.A. Smolka, B.U. Steffen, Reactive, generative, stratified models of probabilistic processes, Information and Computation 121 (1) (1995) 59-80.
59. N. Viswanadham, Y. Narahari, Performance Modeling of Automated Manufacturing Systems, Prentice-Hall Inc, 1992.
60. S.-H. Wu, S.A. Smolka, E.W. Stark, Composition and behaviors for probabilistic I/O automata. Theoretical Computer Science 176 (1-2) (1997) 1-36.