An efficient algorithm for computing bisimulation equivalence

Theoretical Computer Science

Volumn 311, Issue 1-3, 2004, Pages 221-256

  Dovier, Agostino ^a   Piazza, Carla ^a   Policriti, Alberto ^a  

^a UNIVERSITY OF UDINE   (Italy)

Author keywords

Bisimulation; Non well founded sets; OBDDs; Rank based methods; Verification

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DATA STRUCTURES; FUNCTIONS; GRAPH THEORY; OPTIMIZATION; SET THEORY;

BISIMULATION; NON-WELL-FOUNDED SETS; RANK-BASED METHODS; VERIFICATION;

FORMAL LOGIC;

EID: 0346969678     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(03)00361-X     Document Type: Article

References (47)

1. P. Aczel, Non-Well-Founded Sets, CSLI Lecture Notes, Vol. 14, Stanford University Press, Standford, 1988.
2. A. Aziz, V. Sighal, G. Swamy, R. Brayton, Minimizing interacting finite state machines: a compositional approach to language containment, in: Proc. Internat. Conf. on Computer Design (ICCD'94), IEEE Computer Society Press, Silver Spring, MD, 1994, pp. 255-261.
3. Barwise J., Moss L. Hypersets. The Math. Intelligencer. 13(4):1991;31-41.
4. J. Barwise, L. Moss, vicious circles. On the Mathematics of non-well-founded phenomena, CSLI Lecture Notes, Vol. 60, Stanford University Press, Stanford, 1996.
5. J. van Benthem, Modal correspondence theory, Ph.D. Thesis, Universiteit van Amsterdam, Instituut voor Logica en Grondslagenonderzo ek van Exacte Wetenschappen, 1976.
6. R. Bloem, H.N. Gabow, F. Somenzi, An algorithm for strongly connected component analysis in n log n symbolic steps, in: W.A. Hunt Jr., S.D. Johnson, (Eds.), Proc. Internat. Conf. on Formal Methods in Computer-Aided Design (FMCAD'00), Lecture Notes in Computer Science, Vol. 1954, Springer, Berlin, 2000, pp. 37-54.
7. A. Bouajjani, J.C. Fernandez, N. Halbwachs, Minimal model generation, in: E. Clarke, R. Kurshan (Eds.), Proc. Internat. Conf. on Computer Aided Verification (CAV'90), Lecture Notes in Computer Science, Vol. 531, Springer, Berlin, 1990, pp. 197-203.
8. A. Bouali, XEVE, an ESTEREL verification environment, in: A.J. Hu, M.Y. Vardi (Eds.), Proc. Internat. Conf. on Computer Aided Verification (CAV'98), Lecture Notes in Computer Science, Vol. 1427, Springer, Berlin, 1998, pp. 500-504.
9. A. Bouali, R. de Simone, Symbolic bisimulation minimization, in: G. von Bochmann, D.K. Probst (Eds.), Proc. Internat. Conf. on Computer Aided Verification (CAV'92), Lecture Notes in Computer Science, Vol. 663, Springer, Berlin, 1992, pp. 96-108.
10. Bryant R.E. Graph based algorithms for boolean function manipulation. IEEE Trans. Comput. C-35(8):1986;677-691.
11. D. Bustan, O. Grumberg, Simulation based minimization, in: D.A. McAllester (Ed.), Proc. 17th Internat. Conf. on Automated Deduction (CADE'00), Lecture Notes in Computer Science, Vol. 1831, Springer, Berlin, 2000, pp. 255-270.
12. D. Cantone, E.G. Omodeo, A. Policriti, Set theory for computing. From decision procedures to declarative programming with sets, Monographs in Computer Science, Springer, Berlin, 2001.
13. Clarke E.M., Grumberg O., Peled D.A. Model Checking. 1999;The MIT Press, Cambridge, MA.
14. Cleaveland R., Parrow J., Steffen B. The concurrency workbench. a semantics based tool for the verification of concurrent systems ACM Trans. Programming Languages Systems. 15(1):1993;36-72.
15. R. Cleaveland, S. Sims, The NCSU concurrency workbench, in: R. Alur, T.A. Henzinger (Eds.), Proc. Internat. Conf. on Computer Aided Verification (CAV'96), Lecture Notes in Computer Science, LNCS, Vol. 1102, Springer, Berlin, pp. 394-397.
16. Cleaveland R., Sokolsky O. Equivalence and preorder checking for finite-state systems. Bergstra J.A., Ponse A., Smolka S.A. Handbook of Process Algebra. 2001;391-424 North-Holland, Amsterdam.
17. Cortesi A., Dovier A., Quintarelli E., Tanca L. Operational and abstract semantics of the query language G-Log. Theoret. Comput. Sci. 275(1-2):2002;521-560.
18. Dolev D., Klawe M.M., Rodeh M. An. O(n log n) unidirectional distributed algorithm for extrema finding in a circle J. Algorithms. 3(3):1982;245-260.
19. A. Dovier, R. Gentilini, C. Piazza, A. Policriti, Rank-based symbolic bisimulation (and model checking), in: R.J. Guerra, B. de Queiroz (Eds.), WoLLIC'2002, 9th Workshop on Logic, Language, Information and Computation, Electronic Notes in Theoretical Computer Science, Vol. 67, Elsevier, Amsterdam, 2002.
20. A. Dovier, C. Piazza, A. Policriti, A fast bisimulation algorithm, in: G. Berry, H. Comon, A. Finkel (Eds.), Proc. Internat. Conf. on Computer Aided Verification (CAV'01), Lecture Notes in Computer Science, Vol. 2102, Springer, Berlin, 2001, pp. 79-90.
21. J.C. Fernandez, H. Garavel, A. Kerbrat, R. Mateescu, L. Mounier, M. Sighireanu, CADP: a protocol validation and verification toolbox, in: R. Alur, T.A. Henzinger (Eds.), Proc. Internat. Conf. on Computer Aided Verification (CAV'96), Lecture Notes in Computer Science, Vol. 1102, Springer, Berlin, 1996, pp. 437-440.
22. K. Fisler, M.Y. Vardi, Bisimulation and model checking, in: L. Pierre, T. Kropf (Eds.), Proc. Correct Hardware Design and Verification Methods (CHARME'99), Lecture Notes in Computer Science, Vol. 1703, Springer, Berlin, 1999, pp. 338-341.
23. Focardi R., Gorrieri R. The compositional security checker. a tool for the verification of information flow security properties IEEE Trans. Software Eng. 23(9):1997;550-571.
24. Forti M., Honsell F. Set theory with free construction principles. Annali Scuola Normale Superiore Pisa, Cl. Sc. IV(10):1983;493-522.
25. R. Gentilini, C. Piazza, A. Policriti, Simulation as coarsest partition problem, in: J.-P. Katoen, P. Stevens (Eds.), Proc. Tools and Algorithms for the Construction and Analysis of Systems (TACAS-02), Lecture Notes in Computer Science, Vol. 2280, Springer, Berlin, 2002, pp. 415-430.
26. R. Gentilini, C. Piazza, A. Policriti, Computing strongly connected components in a linear number of symbolic steps, in: Proc. of Internat. Symp. on Discrete Algorithms (SODA'03), ACM, New York, 2003, pp. 573-582.
27. Hennessy M., Lin H. Symbolic bisimulations. Theoret. Comput. Sci. 138(2):1995;353-389.
28. M.R. Henzinger, T.A. Henzinger, P.W. Kopke, Computing simulations on finite and infinite graphs, in: Proc. 36th IEEE Symp. on Foundations of Computer Science, (FOCS'1995), IEEE Computer Society Press, Silver Spring, MD, 1995, pp. 453-462.
29. Hirshfeld Y., Jerrum M., Moller F. A polynomial time algorithm for deciding bisimulation equivalence of normed basic parallel processes. Math. Struct. Comput. Sci. 6:1996;251-259.
30. Holzmann G.J. Design and Validation of Computer Protocols. 1991;Prentice-Hall, Englewood Cliffs, NJ.
31. Holzmann G.J. The model checker SPIN. IEEE Trans. Software Eng. 23(5):1997;279-295.
32. Holzmann G.J., Puri A. A minimized automaton representation of reachable states. Software Tools Technol. Transfer. 2(3):1999;270-278.
33. J.E. Hopcroft, An n log n algorithm for minimizing states in a finite automaton, in: Kohavi, Paz (Eds.), Theory of Machines and Computations, Academic Press, New York, 1971, pp. 189-196.
34. Kannellakis P.C., Smolka S.A. CCS expressions, finite state processes, and three problems of equivalence. Inform. Comput. 86(1):1990;43-68.
35. D. Lee, M. Yannakakis, Online minimization of transition systems, in: Proc. 24th ACM Symposium on Theory of Computing (STOC'92), ACM Press, New York, 1992, pp. 264-274.
36. A. Lisitsa, P. Sazonov, V. Yu, Bounded hyperset theory and web-like data bases, in: Gottlob, Leitsch, Mundici (Eds.), Proc. Computational Logic and Proof Theory, 5th Kurt Gödel Colloquium, Lecture Notes in Computer Science, Vol. 1289, Springer, Berlin, 1997, pp. 172-185.
37. McMillan K.L. Symbolic Model Checking: An Approach to the State Explosion Problem. 1993;Kluwer Academic Publishers, Dordrecht.
38. R. Milner, Operational and algebraic semantics of concurrent processes, in: J. van Leeuwen (Ed.), Handbook of Theoretical Computer Science, Elsevier Science, Amsterdam, 1990 (Chapter 19).
39. Paige R., Tarjan R.E., Bonic R. A linear time solution to the single function coarsest partition problem. Theoret. Comput. Sci. 40:1985;67-84.
40. Paige R., Tarjan R.E. Three partition refinement algorithms. SIAM J. Comput. 16(6):1987;973-989.
41. D. Park, Concurrency and automata on infinite sequences, in: P. Deussen (Ed.), Proc. 5th Internat. Conf. on Theoretical Computer Science, Lecture Notes in Computer Science, Vol. 104, Springer, Berlin, 1981, pp. 167-183.
42. F. Rahim, Property-dependent modular model checking application to VHDL with computational results, in: Proc. Internat. Workshop HLDVT, La Jolla, California, 1998.
43. Roscoe A.W. Model checking CSP. Roscoe A.W. A Classical Mind: Essays in Honour of C.A.R. Hoare. 1994;Prentice-Hall, Englewood Cliffs, NJ.
44. J.V. Sanghavi, R.K. Ranjan, R.K. Brayton, A. Sangiovanni-Vincentelli, High performance bdd package based on exploiting memory hierarchy, in: Proc. ACM/IEEE Design Automation Conference, Las Vegas, Nevada, 1996.
45. F. Somenzi, Binary decision diagrams, in: Calculational System Design, NATO Science Series F: Computer and Systems Sciences, Vol. 173, IOS Press, Amsterdam, 1999, pp. 303-366.
46. F. Somenzi, CUDD: CU decision diagram package release 2.3.1, Department of Electrical and Computer Engineering University of Colorado at Boulder, 2001. Available at http://vlsi.colorado.edu/̃fabio/CUDD/cuddIntro.html.
47. Tarjan R.E. Depth first search and linear graph algorithms. SIAM J. Comput. 1(2):1972;146-160.