Abstract
Detection of fair cycles is an important task of many model checking algorithms.When the transition system is represented symbolically, the standard approach to fair cycle detection is the one of Emerson and Lei. In the last decade variants of this algorithm and an alternative method based on strongly connected component decomposition have been proposed.We present a taxonomy of these techniques and compare representatives of each major class on a collection of real-life examples. Our results indicate that the Emerson-Lei procedure is the fastest, but other algorithms tend to generate shorter counter-examples.
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References
R. Bloem, H. N. Gabow, and F. Somenzi. An algorithm for strongly connected component analysis in n log n symbolic steps. In these proceedings.
R. K. Brayton et al. VIS: A system for verification and synthesis. In T. Henzinger and R. Alur, editors, Eighth Conference on Computer Aided Verification (CAV’96), pages 428–432. Springer-Verlag, Rutgers University, 1996. LNCS 1102.
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.
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.
J.W. de Bakker and D. Scott. A theory of programs. Unpublished notes, IBM Seminar, Vienna, 1969.
E. A. Emerson and C. Lei. Modalities for model checking: Branching time logic strikes back. Science of Computer Programming, 8:275–306, 1987.
E. A. Emerson and C.-L. Lei. Efficient model checking in fragments of the propositional mu-calculus. In Proceedings of the First Annual Symposiumof Logic in Computer Science, pages 267–278, June 1986.
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.
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.
R. Hojati, R. K. Brayton, and R. P. Kurshan. BDD-based debugging of designs using language containment and fair CTL. In C. Courcoubetis, editor, Fifth Conference on Computer Aided Verification (CAV’ 93), pages 41–58. Springer-Verlag, Berlin, 1993. LNCS 697.
R. Hojati, H. Touati, R. P. Kurshan, and R. K. Brayton. Efficient ωregular language containment. In Computer Aided Verification, pages 371–382,Montréal, Canada, June 1992.
L. Kantorovitch. The method of successive approximations for functional equations. Acta Mathematica, 71:63–97, 1939.
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.
R. P. Kurshan. Computer-Aided Verification of Coordinating Processes. Princeton University Press, Princeton, NJ, 1994.
O. Lichtenstein and A. Pnueli. Checking that finite state concurrent programs satisfy their linear specification. In Proceedings of the Twelfth Annual ACM Symposium on Principles of Programming Languages,New Orleans, January 1985.
K. L. McMillan. Symbolic Model Checking. Kluwer Academic Publishers, Boston, MA, 1994.
D. M. R. Park. Fixpoint induction and proofs of program properties. Machine Intelligence, 5, 1970.
F. Somenzi. Symbolic state exploration. Electronic Notes in TheoreticalComputer Science, 23, 1999. http://www.elsevier.nl/locate/entcs/volume23.html.
R. Tarjan. Depth first search and linear graph algorithms. SIAM Journal of Computing, 1:146–160, 1972.
A. Tarski. A lattice-theoretic fixpoint theorem and its applications. Pacific Journal of Mathematics, 5:285–309, 1955.
H. J. Touati, R. K. Brayton, and R. P. Kurshan. Testing language containment for ω-automata using BDD’s. In 1991 International Workshop on Formal Methods in VLSI Design, Miami, FL, January 1991.
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.
M. Y. Vardi and P. Wolper. An automata-theoretic approach to automatic program verification. In Proceedings of the First Symposiumon Logic in Computer Science, pages 322–331, Cambridge, UK, June 1986.
A. Xie and P. A. Beerel. Implicit enumeration of strongly connected components. In Proceedings of the International Conference on Computer-AidedDesign, pages 37–40, San Jose, CA, November 1999.
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Ravi, K., Bloem, R., Somenzi, F. (2000). A Comparative Study of Symbolic Algorithms for the Computation of Fair Cycles. In: Hunt, W.A., Johnson, S.D. (eds) Formal Methods in Computer-Aided Design. FMCAD 2000. Lecture Notes in Computer Science, vol 1954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40922-X_10
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DOI: https://doi.org/10.1007/3-540-40922-X_10
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