Optimal state-space lumping in Markov chains

Information Processing Letters

Volumn 87, Issue 6, 2003, Pages 309-315

  Derisavi, Salem ^a   Hermanns, Holger ^b,c   Sanders, William H ^a  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF TWENTE   (Netherlands)

^c SAARLAND UNIVERSITY   (Germany)

Author keywords

Bisimulation; Computational complexity; Lumpability; Markov chains; Splay trees

Indexed keywords

COMPUTATIONAL COMPLEXITY; DATA PROCESSING; NUMERICAL ANALYSIS; TREES (MATHEMATICS);

STATE-SPACE LUMPING;

MARKOV PROCESSES;

EID: 0041466320     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-0190(03)00343-0     Document Type: Article

References (19)

1. Aho A.V., Hopcroft J.E., Ullman J.D. The Design and Analysis of Computer Algorithms. 1974;Addison-Wesley, Reading, MA.
2. Bernardo M., Gorrieri R. A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time. Theoret. Comput. Sci. 202:1998;1-54.
3. Buchholz P. Exact and ordinary lumpability in finite Markov chains. J. Appl. Probab. 31:1994;59-75.
4. Buchholz P. Efficient computation of equivalent and reduced representations for stochastic automata. Internat. J. Comput. Systems Sci. Engrg. 15:(2):2000;93-103.
5. Deavours D.D., Clark G., Courtney T., Daly D., Derisavi S., Doyle J.M., Sanders W.H., Webster P. The Möbius framework and its implementation. IEEE Trans. Software Engrg. 28:(10):2002;956-969.
6. H. Hermanns, Interactive Markov chains, PhD thesis, Friedrich-Alexander-Universität, Erlangen-Nürnberg, 1998.
7. Hermanns H., Siegle M. Bisimulation algorithms for stochastic process algebras and their BDD-based implementation. Katoen J.-P. ARTS'99, 5th Internat. AMAST Workshop on Real-Time and Probabilistic Systems, Vol. 1601. 1999;144-264 Springer, Berlin.
8. Hillston J. A Compositional Approach to Performance Modelling. 1996;Cambridge University Press, Cambridge.
9. Hopcroft J.E. An nlogn algorithm for minimizing states in a finite automaton. Kohavi Z., Paz A. Theory of Machines and Computations. 1971;189-196 Academic Press, New York.
10. Howard R.A. Dynamic Probabilistic Systems, Vol. II: Semi-Markov and Decision Processes. 1971;Wiley, New York.
11. Huynh D.T., Tian L. On some equivalence relations for probabilistic processes. Fund. Inform. 17:1992;211-234.
12. Kanellakis P.C., Smolka S.A. CCS expressions, finite state processes, and three problems of equivalence. Proc. ACM Symposium on Principles of Distributed Computing. 1983;228-240.
13. Kemeney J.G., Snell J.L. Finite Markov Chains. 1960;D. Van Nostrand, New York.
14. Larsen K., Skou A. Bisimulation through probabilistic testing. Inform. and Comput. 94:(1):1991;1-28.
15. Milner R. Communication and Concurrency. 1989;Prentice-Hall, London.
16. Paige R., Tarjan R.E. Three partition refinement algorithms. SIAM J. Comput. 16:(6):1987;973-989.
17. Schweitzer P.J. Aggregation methods for large Markov chains. Iazeolla G., Courtois P.J., Hordijk A. Mathematical Computer Performance and Reliability. 1984;275-302 Elsevier, Amsterdam.
18. Sleator D.D., Tarjan R.E. Self-adjusting binary search trees. J. ACM. 32:(3):1985;652-686.
19. Sumita U., Rieders M. Lumpability and time reversibility in the aggregation-disaggregation method for large Markov chains. Comm. Statist. Stochastic Models. 5:1989;63-81.