On finite-state approximants for probabilistic computation tree logic

Theoretical Computer Science

Volumn 346, Issue 1, 2005, Pages 113-134

  Huth, Michael ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Abstraction; Markov chain; Optimality; Probabilistic model checking

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; FUNCTIONS; MARKOV PROCESSES; SEMANTICS; SET THEORY;

ABSTRACTION; OPTIMALITY; PROBABILISTIC MODEL CHECKING;

PROBABILISTIC LOGICS;

EID: 27744519323     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2005.08.008     Document Type: Conference Paper

References (34)

1. S. Abramsky, and A. Jung Domain Theory S. Abramsky D.M. Gabbay T.S.E. Maibaum Handbook of Logic in Computer Science Vol. 3 1994 Oxford University Press Oxford 1 168
2. T. Ball, B. Cook, S. Das, S.K. Rajamani, Refining approximations in software predicate abstraction, in: Proc. 10th Internat. Conf. on Tools and Algorithms for the Construction and Analysis of Systems, Barcelona, Spain, Lecture Notes in Computer Science, Vol. 2988, Springer, Berlin, 2004, pp. 388-403.
3. T. Ball, A. Podelski, S.K. Rajamani, Boolean and Cartesian abstraction for model checking C programs, in: Proc. Seventh Internat. Conf. on Tools and Algorithms for the Construction and Analysis of Systems, Genova, Italy, Lecture Notes in Computer Science, Vol. 2031, Springer, Berlin, 2001, pp. 268-283.
4. P. Billingsley Probability and Measure third ed. 1995 Wiley-Interscience New York
5. G. Bruns, P. Godefroid, Model checking partial state spaces with 3-valued temporal logics, in: Proc. 11th Conf. on Computer Aided Verification, Trento, Italy, Lecture Notes in Computer Science, Vol. 1633, Springer, Berlin, 1999, pp. 274-287.
6. G. Bruns, P. Godefroid, Generalized model checking: reasoning about partial state spaces, in: Proc. 11th Internat. Conf. on Concurrency Theory, University Park, Pennsylvania, Lecture Notes in Computer Science, Vol. 1877, Springer, Berlin, 2000, pp. 168-182.
7. C. Courcoubetis, and M. Yannakakis The complexity of probabilistic verification J. Assoc. Comput. Mach. 42 4 1995 857 907
8. P. Cousot, and R. Cousot Abstract interpretation: a unified lattice model for static analysis of programs Proc. Fourth ACM Symposium on Principles of Programming Languages 1977 Los Angeles California, ACM Press, New York 238 252
9. D. Dams, Abstract interpretation and partition refinement for model checking, Ph.D. Thesis, Technische Universiteit Eindhoven, The Netherlands, 1996.
10. D. Dams, R. Gerth, and O. Grumberg Abstract interpretation of reactive systems ACM Trans. Programming Languages & Systems 19 2 1997 253 291
11. D. Dams, K. Namjoshi, The existence of finite abstractions for branching time model checking, in: Proc. 19th Annu. IEEE Symp. on Logic in Computer Science, 13-17 July, Turku, Finland, IEEE Computer Society Press, Silver Springs, MD, 2004, pp. 335-344.
12. V. Danos, and J. Desharnais Labelled Markov processes: stronger and faster approximations Proc. 18th Annu. IEEE Symp. on Logic in Computer Science 2003 Ottawa, Canada IEEE Computer Society Press, Silver Springs, MD 341 350
13. V. Danos, J. Desharnais, P. Panangaden, Conditional expectations and the approximation of labelled Markov processes, in: R.M. Amadio, D. Lugiez (Eds.), Proc. 14th Internat. Conf. on Concurrency Theory, Marseille, France, Lecture Notes in Computer Science, Vol. 2761, Springer, Berlin, 2003, pp. 468-482.
14. P.R. D'Argenio, B. Jeannet, H.E. Jensen, and K.G. Larsen Reachability analysis of probabilistic systems by successive refinements L. de Alfaro S. Gilmore PAPM-PROBMIV 2001, Aachen, Germany, Lecture Notes in Computer Science Vol. 2165 2001 Springer Berlin 39 56
15. J. Desharnais, A. Edalat, and P. Panangaden Bisimulation for labelled Markov processes J. Inform. Comput. 179 2 2002 163 193
16. J. Desharnais, V. Gupta, R. Jagadeesan, P. Panangaden, Metrics for labelled Markov systems, in: J.C.M. Baeten, S. Mauw (Eds.), Proc. 10th Internat. Conf. on Concurrency Theory, Eindhoven, The Netherlands, Lecture Notes in Computer Science, Vol. 1664, Springer, Berlin, 1999, pp. 258-273.
17. J. Desharnais, V. Gupta, R. Jagadeesan, and P. Panangaden Approximating labeled Markov processes Proc. 15th Annu. IEEE Symp. on Logic in Computer Science 2000 Santa Barbara, California IEEE Computer Society Press, Silver Springs, MD 95 106
18. J. Desharnais, V. Gupta, R. Jagadeesan, and P. Panangaden The metric analogue of weak bisimulation for probabilistic processes Proc. 17th Annu. IEEE Symp. on Logic in Computer Science 2002 Copenhagen, Denmark IEEE Computer Society Press, Silver Springs, MD 413 422
19. A. Di Pierro, C. Hankin, H. Wiklicky, Quantitative relations and approximate process equivalences, in: Proc. 14th Internat. Conf. on Concurrency Theory, Marseille, France, Lecture Notes in Computer Science, Vol. 2761, Springer, Berlin, 2003, pp. 508-522.
20. M. Franceschet, and M. de Rijke Model checking for hybrid logics Proc. Workshop on Methods for Modalities September 2003 INRIA Lorraine Nancy, France
21. P. Godefroid, M. Huth, R. Jagadeesan, Abstraction-based model checking using modal transition systems, in: Proc. 12th Internat. Conf. on Theory and Practice of Concurrency, BRICS Aalborg, Denmark, Lecture Notes in Computer Science, Vol. 2154, Springer, Berlin, 2001, pp. 426-440.
22. H.A. Hansson, and B. Jonsson A logic for reasoning about time and reliability Formal Aspects Comput. 6 5 1994 512 535
23. M. Huth, Possibilistic and probabilistic abstraction-based model checking, in: H. Hermanns, R. Segala (Eds.), Proc. Second Joint Internat. Workshop PAPM-PROBMIV 2002, Copenhagen, Denmark, Lecture Notes in Computer Science, Vol. 2399, Springer, Berlin, 2002, pp. 115-134.
24. M. Huth, Abstraction and probabilities for hybrid logics, in: A. Cerone, A. Di Pierro (Eds.) Proc. Second Workshop in Quantitative Aspects of Programming Languages, Electronic Notes in Theoretical Computer Science, Vol. 112, Barcelona, Spain, 2004, pp. 61-76.
25. M. Huth, An abstraction framework for mixed non-deterministic and probabilistic systems, in: C. Baier et al. (Eds.), Validation of Stochastic Systems, A Guide to Current Research, Lecture Notes in Computer Science, Vol. 2925, Springer, Berlin, 2004, pp. 419-444.
26. M. Huth, R. Jagadeesan, and D.A. Schmidt Modal transition systems: a foundation for three-valued program analysis D. Sands Proc. 10th European Symp. on Programming 2001 Genova Italy, Springer, Berlin 155 169
27. M. Huth, and M. Kwiatkowska Quantitative analysis and model checking Proc. 12th Annu. IEEE Symp. on Logic in Computer Science 1997 Warsaw, Poland IEEE Computer Society Press, Silver Springs, MD 111 122
28. B. Jonsson, and K.G. Larsen Specification and refinement of probabilistic processes Sixth Annu. IEEE Symp. on Logic in Computer Science 1991 Amsterdam, The Netherlands IEEE Computer Society Press, Silver Springs, MD 266 277
29. D. Kozen Semantics of probabilistic programs Comput. & Syst. Sci. 22 1981 328 350
30. M. Kwiatkowska, Model checking for probability and time: from theory to practice, Invited paper in the 18th Annu. IEEE Symp. on Logic in Computer Science, Ottawa, Canada, IEEE Computer Society Press, Silver Springs, MD, 2003, pp. 351-360.
31. K.G. Larsen, and B. Thomsen A modal process logic Third Annu. IEEE Symp. on Logic in Computer Science 1988 Edinburgh, Scotland IEEE Computer Society Press, Silver Springs, MD 203 210
32. G. Markowsky Chain-complete posets and directed sets with applications Algebra Universalis 6 1 1976 53 68
33. D. Monniaux, Abstract interpretation of programs as Markov decision processes, in: R. Cousot (Ed.), Proc. 10th Internat. Symp. on Static Analysis, San Diego, California, Lecture Notes in Computer Science, Vol. 2694, Springer, Berlin, 2003, pp. 237-254.
34. D.A. Schmidt Structure-preserving binary relations for program abstraction T. Mogensen D. Schmidt I.H. Sudburough The Essence of Computation: Complexity, Analysis, Transformation, Lecture Notes in Computer Science Vol. 2566 2002 Springer Berlin 245 265