Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Three partition refinement algorithms
SIAM Journal on Computing
CCS expressions finite state processes, and three problems of equivalence
Information and Computation
An implementation of an efficient algorithm for bisimulation equivalence
Science of Computer Programming
Design and validation of computer protocols
Design and validation of computer protocols
Online minimization of transition systems (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
The concurrency workbench: a semantics-based tool for the verification of concurrent systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
Algebraic decision diagrams and their applications
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
An n log n algorithm for online BDD refinement
Journal of Algorithms
Bisimulation and Model Checking
CHARME '99 Proceedings of the 10th IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods
XEVE, an ESTEREL Verification Environment
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Symbolic Bisimulation Minimisation
CAV '92 Proceedings of the Fourth International Workshop on Computer Aided Verification
CADP - A Protocol Validation and Verification Toolbox
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
The NCSU Concurrency Workbench
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
An efficient algorithm for computing bisimulation equivalence
Theoretical Computer Science
The Tractability Frontier for NFA Minimization
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
From sequential extended regular expressions to NFA with symbolic labels
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
The tractability frontier for NFA minimization
Journal of Computer and System Sciences
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There has been several attempts over the years to solve the bisimulation minimization problem for finite automata. One of the most famous algorithms is the one suggested by Paige and Tarjan. The algorithm has a complexity of $\mathcal O$(m log n) where m is the number of edges and n is the number of states in the automaton. A bottleneck in the application of the algorithm is often the number of labels which may appear on the edges of the automaton. In this paper we adapt the Paige-Tarjan algorithm to the case where the labels are symbolically represented using Binary Decision Diagrams (BDDs). We show that our algorithm has an overall complexity of ${\mathcal O}(l \cdot m \cdot log{n})$ where ℓ is the size of the alphabet. This means that our algorithm will have the same worst case behavior as other algorithms. However, as shown by our prototype implementation, we get a vast improvement in performance due to the compact representation provided by the BDDs.