Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
On &ohgr;-automata and temporal logic
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
On computing the transitive closure of a state transition relation
DAC '93 Proceedings of the 30th international Design Automation Conference
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Model checking
A New Heuristic for Bad Cycle Detection Using BDDs
Formal Methods in System Design - Special issue on CAV '97
A Comparative Study of Symbolic Algorithms for the Computation of Fair Cycles
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Analysis of Symbolic SCC Hull Algorithms
FMCAD '02 Proceedings of the 4th International Conference on Formal Methods in Computer-Aided Design
Is There a Best Symbolic Cycle-Detection Algorithm?
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
NUSMV: A New Symbolic Model Verifier
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
Efficient omega-Regular Language Containment
CAV '92 Proceedings of the Fourth International Workshop on Computer Aided Verification
Algorithmic Verification of Linear Temporal Logic Specifications
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
The saturation algorithm for symbolic state-space exploration
International Journal on Software Tools for Technology Transfer (STTT) - Special section on Tools and Algorithms for the Construction and Analysis of Systems
Logic and stochastic modeling with SMART
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Depth-first search and linear grajh algorithms
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Reduction Techniques for Model Checking Markov Decision Processes
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Symbolic State-Space Generation of Asynchronous Systems Using Extensible Decision Diagrams
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Advanced features in SMART: the stochastic model checking analyzer for reliability and timing
ACM SIGMETRICS Performance Evaluation Review
Symbolic CTL Model Checking of Asynchronous Systems Using Constrained Saturation
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
DTMC Model Checking by SCC Reduction
QEST '10 Proceedings of the 2010 Seventh International Conference on the Quantitative Evaluation of Systems
Markovian analysis of large finite state machines
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient state classification of finite-state Markov chains
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Implicit enumeration of strongly connected components and an application to formal verification
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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The computation of strongly connected components (SCCs) in discrete-state models is a critical step in formal verification of LTL and fair CTL properties, but the potentially huge number of reachable states and SCCs constitutes a formidable challenge. We consider the problem of computing the set of states in SCCs or terminal SCCs in an asynchronous system. We employ the idea of saturation, which has shown clear advantages in symbolic state-space exploration (Ciardo et al. in Softw Tools Technol Transf 8(1):4---25, 2006; Zhao and Ciardo in Proceedings of 7th international symposium on automated technology for verification and analysis, pp 368---381, 2009), to improve two previously proposed approaches. We use saturation to speed up state exploration when computing each SCC in the Xie-Beerel algorithm, and we compute the transitive closure of the transition relation using a novel algorithm based on saturation. Furthermore, we show that the techniques we developed are also applicable to the computation of fair cycles. Experimental results indicate that the improved algorithms using saturation achieve a substantial speedup over previous BFS algorithms. In particular, with the new transitive closure computation algorithm, up to 10150 SCCs can be explored within a few seconds.