Three partition refinement algorithms
SIAM Journal on Computing
Characterizing finite Kripke structures in propositional temporal logic
Theoretical Computer Science - International Joint Conference on Theory and Practice of Software Development, P
An implementation of an efficient algorithm for bisimulation equivalence
Science of Computer Programming
Re-describing an algorithm by Hopcroft
Theoretical Computer Science
Communication and Concurrency
The Science of Programming
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
CCS expressions, finite state processes, and three problems of equivalence
PODC '83 Proceedings of the second annual ACM symposium on Principles of distributed computing
An n log n algorithm for minimizing states in a finite automaton
An n log n algorithm for minimizing states in a finite automaton
An efficient algorithm for computing bisimulation equivalence
Theoretical Computer Science
Fast brief practical DFA minimization
Information Processing Letters
Simple O(m log n) time Markov chain lumping
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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A new algorithm for bisimilarity minimization of labelled directed graphs is presented. Its time consumption is O (m logn ), where n is the number of states and m is the number of transitions. Unlike earlier algorithms, it meets this bound even if the number of different labels of transitions is not fixed. It is based on refining a partition on states with respect to the labelled transitions. A splitter is a pair consisting of a set in the partition and a label. Earlier algorithms consume lots of time in scanning splitters that have no corresponding relevant transitions. The new algorithm avoids this by maintaining the sets of the corresponding transitions. To facilitate this, a refinable partition data structure with amortized constant time operations is introduced. Detailed pseudocode and correctness proof are presented, as well as some measurements.