On the use of MTBDDs for performability analysis and verification of stochastic systems

Journal of Logic and Algebraic Programming

Volumn 56, Issue 1-2 SPEC., 2003, Pages 23-67

  Hermanns, Holger ^a   Kwiatkowska, Marta ^b   Norman, Gethin ^b   Parker, David ^b   Siegle, Markus ^c  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^c UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Binary decision diagrams; Markov chain; Markov decision process; Model checking; Multi terminal binary decision diagrams; Performability analysis

Indexed keywords

ALGORITHMS; BINARY SEQUENCES; CODES (SYMBOLS); DECISION THEORY; HEURISTIC METHODS; LARGE SCALE SYSTEMS; MARKOV PROCESSES; PROBABILITY; STATE SPACE METHODS;

BINARY DECISION DIAGRAMS (BDD); PERFORMANCE ANALYSIS;

STOCHASTIC PROGRAMMING;

EID: 0038558597     PISSN: 15678326     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1567-8326(02)00066-8     Document Type: Article

References (70)

1. Puterman M. Markov Decision Processes. 1994;Wiley.
2. Courcoubetis C., Yannakakis M. The complexity of probabilistic verification. Journal of the ACM. 42(4):1995;857-907.
3. R. Segala, Modelling and verification of randomized distributed real time systems, Ph.D. thesis, Massachusetts Institute of Technology, 1995.
4. Milner R. Communication and Concurrency. 1989;Prentice Hall.
5. Bolognesi T., Brinksma E. Introduction to the ISO specification language LOTOS. van Eijk P., Vissers C., Diaz M. The Formal Description Technique LOTOS. 1989;23-73 North-Holland, Amsterdam.
6. N. Götz, U. Herzog, M. Rettelbach, Multiprocessor and distributed system design: The integration of functional specification and performance analysis using stochastic process algebras, in: Proceedings of the 16th International Symposium on Computer Performance Modelling, Measurement and Evaluation, PERFORMANCE 1993, Tutorial, vol. 729 of Lecture Notes in Computer Science, Springer, 1993, pp. 121-146.
7. Hillston J. A Compositional Approach to Performance Modelling. 1996;Cambridge University Press.
8. Hermanns H., Herzog U., Katoen J.-P. Process algebra for performance evaluation. Theoretical Computer Science. 274(1-2):2002;43-87.
9. P. Courtois, Decomposability, queueing and computer system applications, ACM monograph series, 1977.
10. B. Plateau, On the synchronization structure of parallelism and synchronization models for distributed algorithms, in: Proceedings of the ACM Sigmetrics Conference on Measurement and Modeling of Computer Systems, Austin, TX, 1985, pp. 147-154.
11. Buchholz P. A class of hierarchical queueing networks and their analysis. Queueing Systems. 15:1994;59-80.
12. Hermanns H., Katoen J. Automated compositional Markov chain generation for a plain-old telephony system. Science of Computer Programming. 36(1):1999;97-127.
13. M. Siegle, Structured Markovian performance modelling with automatic symmetry exploitation, in: G. Haring, H. Wabnig (Eds.), Short Papers and Tool Descriptions Proceedings of the 7th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, Vienna, Austria, 1994, pp. 77-81.
14. Bryant R. Graph-based algorithms for boolean function manipulation. IEEE ToC. C-35(8):1986;677-691.
15. R. Bahar, E. Frohm, C. Gaona, G. Hachtel, E. Macii, A. Pardo, F. Somenzi, Algebraic decision diagrams and their applications, in: ICCAD-93: International Conference on Computer-Aided Design, ACM/IEEE, Santa Clara, CA, 1993, pp. 188-191, also available in Formal Methods in System Design 10 (2/3) 1997.
16. E. Clarke, M. Fujita, P. McGeer, K. McMillan, J. Yang, X. Zhao, Multi-terminal binary decision diagrams: an efficient data structure for matrix representation, in: Proceedings of International Workshop on Logic Synthesis (IWLS'93), Tahoe City, 1993, pp. 6a:1-15, also available in Formal Methods in System Design 10 (2/3) (1997) 149-169.
17. Hansson H., Jonsson B. A framework for reasoning about time and reliability. Proceedings of 10th IEEE Real-Time Systems Symposium. 1990;102-111 IEEE Computer Society Press, Orlando, FL.
18. C. Baier, B. Haverkort, H. Hermanns, J.-P. Katoen, On the logical characterisation of performability properties, in: ICALP, vol. 1853 of Lecture Notes in Computer Science, Springer, 2000, pp. 780-792.
19. Hermanns H., Herzog U., Mertsiotakis V. Stochastic process algebras - between LOTOS and Markov chains. Computer Networks and ISDN (CNIS). 30(9-10):1998;901-924.
20. H. Hermanns, Interactive Markov chains, Lecture Notes in Computer Science, vol. 2428, Springer, 2002.
21. Bernardo M., Gorrieri R. A tutorial on EMPA: a theory of concurrent processes with nondeterminism, priorities, probabilities and time. Theoretical Computer Science. 202:1998;1-54.
22. M. Bravetti, M. Bernardo, Compositional asymmetric cooperations for process algebras with probabilities, priorities, and time, in: Proceedings of the 1st International Workshop on Models for Time Critical Systems (MTCS 2000), Electronic Notes in Theoretical Computer Science 39 (3), State College (PA), 2000.
23. Olderog E.-R., Hoare C. Specification-oriented semantics for communicating processes. Acta Informatica. 23(1):1986;9-66.
24. G. Plotkin, A structural approach to operational semantics, technical report, Computer Science Department FN-19, DAIMI, Aarhus University, September 1981.
25. A. Bianco, L. de Alfaro, Model checking of probabilistic and nondeterministic systems, in: P. Thiagarajan (Ed.), Proceedings of Foundations of Software Technology and Theoretical Computer Science, vol. 1026 of Lecture Notes in Computer Science, Springer-Verlag, 1995, pp. 499-513.
26. Baier C., Kwiatkowska M. Model checking for a probabilistic branching time logic with fairness. Distributed Computing. 11:1998;125-155.
27. Hart S., Sharir M., Pnueli A. Termination of probabilistic concurrent programs. ACM Transactions on Programming Languages and Systems. 5:1983;356-380.
28. L. de Alfaro, From fairness to chance, in: C. Baier, M. Huth, M. Kwiatkowska, M. Ryan (Eds.), Proceedings of First International Workshop on Probabilistic Methods in Verification (PROBMIV'98), vol. 22 of Electronic Notes in Theoretical Computer Science, 1998.
29. E. Clarke, E. Emerson, A. Sistla, Automatic verification of finite-state concurrent systems using temporal logics, in: 10th ACM Symposium on Principles of Programming Languages, 1983, pp. 24-26, the full version is available in ACM Transactions on Programming Languages and Systems 1(2), 1986.
30. C. Baier, On algorithmic verification methods for probabilistic systems, Habilitation thesis, Fakultät für Mathematik & Informatik, Universität Mannheim, 1999.
31. L. de Alfaro, Stochastic transition systems, in: D. Sangiorgi, R. de Simone (Eds.), Proceedings of CONCUR'98, Lecture Notes in Computer Science, Springer-Verlag, 1998, pp. 423-438.
32. L. de Alfaro, M. Kwiatkowska, G. Norman, D. Parker, R. Segala, Symbolic model checking for probabilistic processes using MTBDDs and the Kronecker representation, in: S. Graf, M. Schwartzbach (Eds.), TACAS'2000, LNCS 1785, Berlin, 2000, pp. 395-410.
33. G. Ciardo, R. Zijal, Well-defined stochastic Petri nets, in: MASCOTS, 1996, pp. 278-284.
34. Qureshi M., Sanders W., van Moorsel A., German R. Algorithms for the generation of state-level representations of stochastic activity networks with general reward structures. IEEE Transactions on Software Engineering. 22(9):1996;603-614.
35. D. Deavours, W. Sanders, An efficient well-specified check, in: P. Bucholz, M. Silva (Eds.), Proceedings of the 8th International Workshop on Petri Nets and Performance Models (PNPM '99), Zaragoza, Spain, 1999, pp. 124-133.
36. H. Hermanns, M. Siegle, Bisimulation algorithms for stochastic process algebras and their BDD-based implementation, in: J.-P. Katoen (Ed.), ARTS'99, 5th International AMAST Workshop on Real-Time and Probabilistic Systems, vol. 1601 of Lecture Notes in Computer Science, Springer, 1999, pp. 144-264.
37. Ajmone Marsan M., Balbo G., Conte G. A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Transactions on Computer Systems. 2(2):1984;93-122.
38. Ajmone Marsan M., Balbo G., Conte G., Donatelli S., Franceschinis G. Modelling with generalized stochastic Petri nets. 1995;Wiley.
39. A. Shiryaev, Probability, 2nd edition, vol. 95 of Graduate Texts in Mathematics, Springer, 1996.
40. Stewart W. Introduction to the Numerical Solution of Markov Chains. 1994;Princeton University Press.
41. Jensen A. Markoff chains as an aid in the study of Markoff processes. Skand. Aktuarietiedskr. 36:1953;87-91.
42. Grassmann W. Transient solutions in Markovian queues. European Journal of Operational Research. 1:1977;396-402.
43. E. Clarke, K. McMillan, X. Zhao, M. Fujita, J. Yang, Spectral transforms for large boolean functions with applications to technology mapping, in: 30th Design Automation Conference, ACM/IEEE, 1993, pp. 54-60.
44. K. Brace, R. Rudell, R. Bryant, Efficient implementation of a BDD package, in: 27th ACM/IEEE Design Automation Conference, 1990, pp. 40-45.
45. Enders R., Filkorn T., Taubner D. Generating BDDs for symbolic model checking in CCS. Distributed Computing. 6(3):1993;155-164.
46. McMillan K. Symbolic Model Checking. 1993;Kluwer Academic Publishers.
47. M. Kwiatkowska, G. Norman, D. Parker, R. Segala, Symbolic model checking of concurrent probabilistic systems using MTBDDs and Simplex, Tech. rep., School of Computer Science, University of Birmingham, 1999.
48. M. Kwiatkowska, G. Norman, D. Parker, PRISM: Probabilistic symbolic model checker, in: T. Field, P. Harrison, J. Bradley, U. Harder (Eds.), Proceedings of 12th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation (TOOLS'02), vol. 2324 of LNCS, Springer, 2002, pp. 200-204.
49. F. Somenzi, Cudd: Colorado university decision diagram package, release 2.3.0, user's Manual and Programmer's Manual, http://vlsi.colorado.edu/̃ fabio, September 1998.
50. R. Alur, T. Henzinger, Reactive modules, in: Proceedings of 11th Annual IEEE Symposium on Logic in Computer Science (LICS'96), IEEE Computer Society Press, 1006, pp. 207-218.
51. E. Frank, Codierung und numerische analyse von transitionssystemen unter verwendung von MTBDDs, student's thesis, Universität Erlangen-Nürnberg, IMMD 7, 1999 (in German).
52. E. Frank, Erweiterung eines MTBDD-basierten Werkzeugs für die Analyse stochastischer Transitionssysteme, Tech. Report Informatik 7, no. 01/00, Universität Erlangen-Nürnberg, January 2000 (in German).
53. Hermanns H., Herzog U., Klehmet U., Mertsiotakis V., Siegle M. Compositional performance modelling with the TIPPtool. Performance Evaluation. 39(1-4):2000;5-35.
54. C. Kelley, Iterative Methods for linear and nonlinear systems, Series on Frontiers in Applied Mathematics, SIAM, 1995.
55. Ibe O., Trivedi K. Stochastic Petri net models of polling systems. IEEE Journal on Selected Areas in Communications. 8(9):1990;1649-1657.
56. H. Hermanns, J. Meyer-Kayser, M. Siegle, Multi terminal binary decision diagrams to represent and analyse continuous time Markov chains, in: B. Plateau, W. Stewart, M. Silva (Eds.), 3rd International Workshop on the Numerical Solution of Markov Chains, Prensas Universitarias de Zaragoza, 1999, pp. 188-207.
57. Aspnes J., Herlihy M. Fast randomized consensus using shared memory. Journal of Algorithms. 11(3):1990;441-460.
58. M. Vardi, Automatic verification of probabilistic concurrent finite state programs, in: Proceedings of IEEE Symposium on Foundations of Computer Science (FOCS'85), 1985, pp. 327-338.
59. Bollig B., Wegener I. Improving the variable ordering of OBDDs is NPcomplete. IEEE Transactions on Computers. 45(9):1996;993-1006.
60. S. Tani, K. Hamaguchi, S. Yajima, The complexity of optimal variable ordering of a shared binary decision diagram, in: Proceedings of 45th ISAAC, vol. 762 of Lecture Notes in Computer Science, Springer, 1993, pp. 389-398.
61. R. Rudell, Dynamic variable ordering for ordered binary decision diagrams, in: Proceedings of IEEE ICCAD'93, 1993, pp. 42-47.
62. M. Fujita, Y. Matsunaga, T. Kakuda, On variable ordering of binary decision diagrams for the application of multi-level logic synthesis, in: Proceedings of European Design Automation Conference (EDAC 91), IEEE Computer Society Press, 1991, pp. 50-54.
63. J. Bern, C. Meinel, A. Slobodova, Global rebuilding of OBDD's - tunneling memory requirement maxima, in: P. Wolper (Ed.), Proceedings of International Conference On Computer Aided Verification, vol. 939 of Lecture Notes in Computer Science, Springer-Verlag, 1995, pp. 4-15.
64. D. Parker, Implementation of symbolic model checking for probabilistic systems, Ph.D. thesis, School of Computer Science, University of Birmingham, submitted.
65. Kemeny J., Snell J. Finite Markov Chains. 1976;Springer.
66. Larsen K., Skou A. Bisimulation through probabilistic testing. Information and Computation. 94(1):1991;1-28.
67. Clarke E.M., Jha S., Enders R., Filkorn T. Exploiting symmetry in temporal logic model checking. Formal Methods in System Design. 9(1/2):1996;77-104.
68. J. Katoen, M. Kwiatkowska, G. Norman, D. Parker, Faster and symbolic CTMC model checking, in: L. de Alfaro, S. Gilmore (Eds.), Proceedings of Process Algebra and Probabilistic Methods (PAPM-PROBMIV 2001), vol. 2165 of Lecture Notes in Computer Science, Springer, 2001, pp. 23-38.
69. M. Kwiatkowska, G. Norman, D. Parker, Probabilistic symbolic model checking with PRISM: a hybrid approach, in: J.-P. Katoen, P. Stevens (Eds.), Proceedings of 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS'02), vol. 2280 of LNCS, Springer, 2002, pp. 52-66.
70. P. D'Argenio, B. Jeannet, H. Jensen, K. Larsen, Reachability Analysis of Probabilistic Systems by Successive Refinements, in: L. de Alfaro, S. Gilmore (Eds.), Process Algebra and Probabilistic Methods. Joint International Workshop PAPMPROBMIV 2001, Springer, LNCS 2165, 2001, pp. 39-56.