Abstract
Although there are many efficient algorithms for calculating the simulation preorder on finite Kripke structures, only two have been proposed of which the space complexity is of the same order as the size of the output of the algorithm. Of these, the one with the best time complexity exploits the representation of the simulation problem as a generalised coarsest partition problem. It is based on a fixed-point operator for obtaining a generalised coarsest partition as the limit of a sequence of partition pairs. We show that this fixed-point theory is flawed, and that the algorithm is incorrect. Although we do not see how the fixed-point operator can be repaired, we correct the algorithm without affecting its space and time complexity.
This is an extended abstract; all proofs are omitted. They can be found in the full version [10].
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References
Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. Journal of the ACM 42(1), 232–268 (1995)
Bloom, B., Paige, R.: Transformational design and implementation of a new efficient solution to the ready simulation problem. Science of Computer Programming 24(3), 189–220 (1995)
Bustan, D., Grumberg, O.: Simulation-based minimization. ACM Transactions on Computational Logic 4(2), 181–206 (2003)
Courcoubetis, C., Vardi, M.Y., Wolper, P., Yannakakis, M.: Memory efficient algorithms for the verification of temporal properties. In: Clarke, E., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 233–242. Springer, Heidelberg (1991)
Dams, D., Grumberg, O., Gerth, R.: Generation of reduced models for checking fragments of CTL. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 479–490. Springer, Heidelberg (1993)
Emerson, E.A., Halpern, J.Y.: ”Sometimes” and ”Not Never” revisited: On branching versus linear time temporal logic. Journal of the ACM 33(1), 151–178 (1986)
Evangelista, S., Pradat-Peyre, J.-F.: Memory efficient state space storage in explicit software model checking. In: Godefroid, P. (ed.) SPIN 2005. LNCS, vol. 3639, pp. 43–57. Springer, Heidelberg (2005)
Gentilini, R., Piazza, C., Policriti, A.: From bisimulation to simulation: Coarsest partition problems. Journal of Automated Reasoning 31(1), 73–103 (2003)
Gentilini, R., Piazza, C., Policriti, A.: From bisimulation to simulation: Coarsest partition problems. RR 12-2003, Dep. of Computer Science, University of Udine, Italy (2003)
van Glabbeek, R.J., Ploeger, B.: Correcting a space-efficient simulation algorithm. CS-Report 08-06, Eindhoven University of Technology (2008)
Groote, J.F., Vaandrager, F.W.: Structured operational semantics and bisimulation as a congruence. Information and Computation 100(2), 202–260 (1992)
Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing simulations on finite and infinite graphs. In: 36th Annual Symposium on Foundations of Computer Science (FOCS 1995), pp. 453–462. IEEE Computer Society Press, Los Alamitos (1995)
Holzmann, G.J.: An improved protocol reachability analysis technique. Software Practice and Experience 18(2), 137–161 (1988)
Kozen, D.: Results on the propositional μ-calculus. Theoretical Computer Science 27, 333–354 (1983)
Kucera, A., Jancar, P.: Equivalence-checking on infinite-state systems: Techniques and results. Theory and Practice of Logic Programming 6(3), 227–264 (2006)
Loiseaux, C., Graf, S., Sifakis, J., Bouajjani, A., Bensalem, S.: Property preserving abstractions for the verification of concurrent systems. Formal Methods in System Design 6(1), 11–44 (1995)
Park, D.M.R.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)
Ranzato, F., Tapparo, F.: A new efficient simulation equivalence algorithm. In: Proc. 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007), pp. 171–180. IEEE Computer Society Press, Los Alamitos (2007)
Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time. In: Proc. 5th Annual ACM Symposium on Theory of Computing (STOC 1973), pp. 1–9. ACM, New York (1973)
Tan, L., Cleaveland, R.: Simulation revisited. In: Margaria, T., Yi, W. (eds.) ETAPS 2001 and TACAS 2001. LNCS, vol. 2031, pp. 480–495. Springer, Heidelberg (2001)
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van Glabbeek, R., Ploeger, B. (2008). Correcting a Space-Efficient Simulation Algorithm. In: Gupta, A., Malik, S. (eds) Computer Aided Verification. CAV 2008. Lecture Notes in Computer Science, vol 5123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70545-1_49
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