Verifying probabilistic programs using a hoare like logic

International Journal of Foundations of Computer Science

Volumn 13, Issue 3, 2002, Pages 315-340

  Den Hartog, J I ^a   De Vink, E P ^b  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b KPN RESEARCH   (Netherlands)

Author keywords

Hoare logic; Probabilistic predicates; Probability; Program verification; Randomized algorithms

Indexed keywords

EID: 4944266584     PISSN: 01290541     EISSN: None     Source Type: Journal    
DOI: 10.1142/S012905410200114X     Document Type: Conference Paper

References (29)

1. L. de Alfaro. Formal Verification of Probabilistic Systems. PhD thesis, Stanford University, 1997.
2. N. Alon, J.H. Spencer, and P. Erdos. The Probabilistic Method. Series in Discrete Mathematics and Optimization. Wiley, 1992.
3. S. Andova. Process algebra with probabilistic choice. In J.-P. Katoen, editor, Proceedings ARTS'99, pages 111-129, Bamberg, 1999. LNCS 1601.
4. K.R. Apt and E.-R. Olderog. Verification of Sequential and Concurrent Programs. Texts and Monographs in Computer Science. Springer, 1991.
5. J.CM. Baeten and J. A. Bergstra. Process algebra with partial choice. In B. Jonsson and J. Parrow, editors, Proc. CONCUR'9l pages 465-480. LNCS 836, 1994.
6. C. Baier, M.Z. Kwiatkowska, and G. Norman. Computing probability bounds for linear time formulas over concurrent Markov chains. In Proc. PROBMIV98. ENTCS 22, 1999.
7. J.W. de Bakker. Mathematical Theory of Program Correctness. Series in Computer Science. Prentice-Hall International, 1980.
8. S. A. Cook. Soundness and completeness of an axiom system for program verification. SI AM Journal of Computing, 7(l):70-90, 1978.
9. P.R. D'Argenio. Algebras and Automata for Timed and Stochastic Systems. PhD thesis, University of Twente, 1999.
10. P.R. D'Argenio, J.-P. Katoen, and E. Brinksma. A compositional approach to generalised semi-Markov processes. In Proc. WODES'98, Caligari. IEE, 1998.
11. N. Francez. Program Verification. Addison-Wesley, 1992.
12. 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.
13. J.I. den Hartog. Probabilistic Extensions of Semantical Models. PhD thesis, Vrije Universiteit Amsterdam, 2002. To appear.
14. J.I. den Hartog and E.P. de Vink. Mixing up nondeterminism and probability: A preliminary report. In Proc. PROBMIV98. ENTCS 22, 1999.
15. V. Hartonas-Garmhausen. Probabilistic Symbolic Modelchecking with Engineering Models and Applications. PhD thesis, Carnegie Mellon University, 1998.
16. H. Hermanns. Interactive Markov Chains. PhD thesis, University of Erlangen-Nurnberg, July 1998.
17. C.A.R. Hoare. An axiomatic basis for computer programming. Communications of the ACM, 12:576-580, 1969.
18. J. Hooman. Program design in PVS. In Proc. Workshop on Tool Support for System Development and Verification, June 1996.
19. M. Huth and M.Z. Kwiatkowska. Quantitive analysis and model checking. In Proc. LICS'97, pages 111-122, Warzaw, 1997.
20. C. Jones. Probabilistic Nondeterminism. PhD thesis, ECS-LFCS-90-105, University of Edinburgh, 1990.
21. D. Kozen. A probabilistic PDL. Journal of Computer and System Sciences, 30:162-178, 1985.
22. K.G. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94:1-28, 1991.
23. C. Morgan and A. Mclver. pGCL: formal reasoning for random algorithms. Proc. WOFACS 1998, Special Issue of the South African Computer Journal, 22, 1999.
24. C. Morgan, A. Mclver, and K. Seidel. Probabilistic predicate transformers. ACM Transactions on Programming Languages and Systems, 18:325-353, 1996.
25. R. Motwani and P. Raghavan. Randomized Algorithms. CUP, 1995.
26. M. Nunez, D. de Prutos, and L. Liana. Acceptance trees for probabilistic processes. In I. Lee and S.A. Smolka, editors, Proc. CONCUR'95, pages 249-263. LNCS 962, 1995.
27. A. Pnueli and L.D. Zuck. Probabilistic verification. Information and Computation, 103:1-29, 1993.
28. R. Segala. Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Massachusetts Institute of Technology, 1995.
29. S.-H. Wu, S.A. Smolka, and E.W. Stark. Composition and behavior of probabilistic I/O automata. Theoretical Computer Science, 176:1-38, 1999.