Program construction and verification
Program construction and verification
Three partition refinement algorithms
SIAM Journal on Computing
Re-describing an algorithm by Hopcroft
Theoretical Computer Science
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Optimal state-space lumping in Markov chains
Information Processing Letters
Solution of large markov models using lumping techniques and symbolic data structures
Solution of large markov models using lumping techniques and symbolic data structures
The GreatSPN tool: recent enhancements
ACM SIGMETRICS Performance Evaluation Review
Bisimilarity Minimization in O(m logn) Time
PETRI NETS '09 Proceedings of the 30th International Conference on Applications and Theory of Petri Nets
Lumping partially symmetrical stochastic models
Performance Evaluation
Efficient CTMC model checking of linear real-time objectives
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
On the complexity of computing probabilistic bisimilarity
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Weighted lumpability on markov chains
PSI'11 Proceedings of the 8th international conference on Perspectives of System Informatics
Lumping and reversed processes in cooperating automata
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
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In 2003, Derisavi, Hermanns, and Sanders presented a complicated O(m logn) time algorithm for the Markov chain lumping problem, where n is the number of states and m the number of transitions in the Markov chain. They speculated on the possibility of a simple algorithm and wrote that it would probably need a new way of sorting weights. In this article we present an algorithm of that kind. In it, the weights are sorted with a combination of the so-called possible majority candidate algorithm with any O(k logk) sorting algorithm. This works because, as we prove in the article, the weights consist of two groups, one of which is sufficiently small and all weights in the other group have the same value. We also point out an essential problem in the description of the earlier algorithm, prove the correctness of our algorithm in detail, and report some running time measurements.