Abstract
This paper presents an efficient model checking algorithm for one–safe time Petri nets and a timed temporal logic. The approach is based on the idea of (1) using only differences of timing variables to be able to construct a finite representation of the set of all reachable states and (2) further reducing the size of this representation by exploiting the concurrency in the net. This reduction of the state space is possible, because the considered linear–time temporal logic is stuttering invariant. The firings of transitions are only partially ordered by causality and a given formula; therefore the order of firings of independent transitions is irrelevant, and only one of several equivalent interleavings has to be generated for the evaluation of the given formula. In this paper the theory of timing verification with time Petri nets and temporal logic is presented, a concrete model checking algorithm is developed and proved to be correct, and some experimental results demonstrating the efficiency of the method are given.
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References
R. Alur, C. Courcoubetis, and D. Dill, “Model-checking for real-time systems,” Proc. of 5th IEEE Logic in Computer Science, pp. 414-425, 1990.
R. Alur and T. A. Henzinger, “A really temporal logic,” Proc. of 30th IEEE Foundations of Computer Science, pp. 164-169, 1989.
J. R. Burch, E. M. Clarke, D. L. Dill, L. J. Hwang, and K. L. McMillan, “Symbolic model checking: 1020 states and beyond,” Academic Press, Vol. 98, No. 2, pp. 142-170, 1992.
B. Berthomieu and M. Diaz, “Modeling and verification of time dependent systems using time Petri nets,” IEEE Trans. on Software Eng., Vol. 17, No. 3, pp. 259-273, 1991.
E. M. Clarke, E. A. Emerson, and A. P. Sistla, “Automatic verification of finite-state concurrent systems using temporal logic specifications,” ACM Trans. on Programming Languages and Systems, Vol. 8, No. 2, pp. 244-263, 1986
J. W. de Bakker et al. (ed), editor, Real time-Theory in Practice, Proc. REX Workshop, Springer Lecture Notes in Computer Science 600, 1992.
R. Gerth, R. Kuiper, D. Peled, and W. Penczek, “A partial order approach to branching time logic model checking,” Internal report, 1994.
P. Godefroid, “Using partial orders to improve automatic verification methods,” Proc. of Workshop on Computer Aided Verification, 1990.
T. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine, “Symbolic model checking for real-time systems,” 7th IEEE Logic in Computer Science, pp. 394-406, 1992.
F. Jahanian and A. K. Mok, “ A graph-theoretic approach for timing analysis and its implementation,” IEEE Trans. Comput., Vol. C-36, No. 8, pp. 961-975, 1987.
S. Katz and D. Peled, “Defining conditional independence using collapses,” Semantics for concurrency , BCS-FACS Workshop , M. Kwiatkowska (ed.), Springer, 1
O. Lichtenstein and A. Pnueli, “Checking that finite state concurrent programs satisfy their linear specifi-cation,” Proc. 12th Principles of Programming Languagges, pp. 97-107, 1985.
P. Merlin and D. J. Faber, “Recoverability of communication protocols,” IEEE Trans. on Communication, Vol. COM-24, No. 9, pp. 381-404, 1976.
J-L. Roux and B. Berthomieu, “Verification of a local area network protocol with Tina, a software package for time Petri nets,” 7th European Workshop on Application and Theory of Petri Nets, pp. 183-205, 1986.
P. Starke, Analyse von Petri-Netz Modellen, Teubner, Stuttgart, 1990.
A. Valmari, “A stubborn attack on state explosion,” Proc. of Workshop on Computer-Aided Verification, 1990.
T. Yoneda, K. Nakade, and Y. Tohma, “A fast timing verification method based on the independence of units,” Proc. of 19th International Symposium on Fault-tolerant Computing, pp. 134-141, 1989.
T. Yoneda, Y. Tohma, and Y. Kondo, “Acceleration of timing verification method based on time Petri nets,” Systems and Computers in Japan, Vol. 22, No. 12, pp. 37-52, 1991.
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Yoneda, T., Schlingloff, B. Efficient Verification of Parallel Real–Time Systems. Formal Methods in System Design 11, 187–215 (1997). https://doi.org/10.1023/A:1008682131325
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DOI: https://doi.org/10.1023/A:1008682131325