An algorithm for strongly connected component analysis in n log n symbolic steps

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1954, Issue , 2000, Pages 37-54

  Bloem, Roderick ^a   Gabow, Harold N ^a   Somenzi, Fabio ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; COMPUTER AIDED DESIGN; FORMAL METHODS;

COMPLEXITY BOUNDS; EMERSON; PREIMAGE COMPUTATION; QUADRATIC BOUND; STREETT AUTOMATA; STRONGLY CONNECTED COMPONENT; SYMBOLIC ALGORITHMS;

ALGORITHMS;

EID: 84947241825     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: None     Document Type: Conference Paper

References (28)

1. R. K. Brayton et al. VIS. In Formal Methods in Computer Aided Design, pages 248-256. Springer-Verlag, Berlin, November 1996. LNCS 1166.
2. R. Bloem, K. Ravi, and F. Somenzi. Efficient decision procedures for model checking of linear time logic properties. In N. Halbwachs and D. Peled, editors, Eleventh Conference on Computer Aided Verification (CAV'99), pages 222-235. Springer-Verlag, Berlin, 1999. LNCS 1633.
3. R. E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers, C-35(8): 677-691, August 1986.
4. J. R. Büchi. On a decision method in restricted second order arithmetic. In Proceedings of the 1960 International Congress on Logic, Methodology, and Philosophy of Science, pages 1-11. Stanford University Press, 1962.
5. E. M. Clarke, E. A. Emerson, and A. P. Sistla. Automatic verification of finite state concurrent systems using temporal logic specifications. ACM Transaction on Programming Languages and Systems, 8(2): 244-263, 1986.
6. E. Clarke, O. Grumberg, K. McMillan, and X. Zhao. Efficient generation of counterexamples and witnesses in symbolic model checking. In Proceedings of the Design Automation Conference, pages 427-432, San Francisco, CA, June 1995.
7. E. M. Clarke, O. Grumberg, and D. A. Peled. Model Checking. MIT Press, Cambridge, MA, 1999.
8. E. A. Emerson and C.-L. Lei. Efficient model checking in fragments of the propositional mu-calculus. In Proceedings of the First Annual Symposium of Logic in Computer Science, pages 267-278, June 1986.
9. E. A. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8: 275-306, 1987.
10. S. Even and Y. Shiloach. An online edge-deletion problem. Journal of the Association for Computing Machinery, 28(1): 1-4, January 1981.
11. R. H. Hardin, Z. Har'El, and R. P. Kurshan. COSPAN. In Eighth Conference on Computer Aided Verification (CAV '96), pages 423-427. Springer-Verlag, 1996. LNCS 1102.
12. R. H. Hardin, R. P. Kurshan, S. K. Shukla, and M. Y. Vardi. A new heuristic for bad cycle detection using BDDs. In O. Grumberg, editor, Ninth Conference on Computer Aided Verification (CAV'97), pages 268-278. Springer-Verlag, Berlin, 1997. LNCS 1254.
13. G. H. Hardy, J. E. Littlewood, and G. Pólya. Inequalities. Cambridge University Press, 1952.
14. R. Hojati, T. R. Shiple, R. Brayton, and R. Kurshan. A unified approach to language containment and fair CTL model checking. In Proceedings of the Design Automation Conference, pages 475-481, June 1993.
15. M. R. Henzinger and J. A. Telle. Faster algorithms for the nonemptiness of Streett automata and for communication protocol pruning. In R. Karlsson and A. Lingas, editors, Algorithm Theory: SWAT'96, pages 16-27. Springer-Verlag, Berlin, 1996. LNCS 1097.
16. R. Hojati, H. Touati, R. P. Kurshan, and R. K. Brayton. Efficient ω-regular language containment. In Computer Aided Verification, pages 371-382, Montréal, Canada, June 1992.
17. Y. Kesten, A. Pnueli, and L.-o. Raviv. Algorithmic verification of linear temporal logic specifications. In International Colloquium on Automata, Languages, and Programming (ICALP-98), pages 1-16, Berlin, 1998. Springer. LNCS 1443.
18. R. P. Kurshan. Computer-Aided Verification of Coordinating Processes. Princeton University Press, Princeton, NJ, 1994.
19. K. McMillan. Class project on BDD-based verification. Private Communication, E. M. Clarke, 1987.
20. K. L. McMillan. Symbolic Model Checking. Kluwer Academic Publishers, Boston, MA, 1994.
21. K. L. McMillan. Verification of infinite state systems by compositional model checking. In Correct Hardware Design and Verification Methods (CHARME'99), pages 219-233, Berlin, September 1999. Springer-Verlag. LNCS 1703.
22. K. Ravi, R. Bloem, and F. Somenzi. A comparative study of symbolic algorithms for the computation of fair cycles. In these proceedings.
23. G. Rozenberg and A. Salomaa, editors. Handbook of Formal Languages. Springer, Berlin, 1997.
24. R. S. Streett. Propositional dynamic logic of looping and converse is elementarily decidable. Information and Control, 54: 121-141, 1982.
25. R. Tarjan. Depth first search and linear graph algorithms. SIAM Journal of Computing, 1: 146-160, 1972.
26. H. J. Touati, R. K. Brayton, and R. P. Kurshan. Testing language containment for ω-automata using BDD's. Information and Computation, 118(1): 101-109, April 1995.
27. W. Thomas. Languages, automata, and logic. In Rozenberg and Salomaa [RS97], chapter 7, Vol. 3, pages 389-455.
28. A. Xie and P. A. Beerel. Implicit enumeration of strongly connected components. In Proceedings of the International Conference on Computer-Aided Design, pages 37-40, San Jose, CA, November 1999.