Reduction rules for time Petri nets
Tóm tắt
The goal of net reduction is to increase the effectiveness of Petri-netbased real-time program analysis. Petri-net-based analysis, like all reachabilitybased methods, suffers from the state explosion problem. Petri net reduction is one key method for combating this problem. In this paper, we extend several rules for the reduction of ordinary Petri nets to work with time Petri nets. We introduce a notion of equivalence among time Petri nets, and prove that our reduction rules yield equivalent nets. This notion of equivalence guarantees that crucial timing and concurrency properties are preserved.
Tài liệu tham khảo
Azema, P., Juanole, G., Sanchis, E., Montbernard, M.: Specification and verification of distributed systems using Prolog Interpreted Petri nets. In: Proc. 7th Int. Conf. on Software Engineering, pp. 510–518, Orlando, Florida, 1984
Berthelot, G.: Transformations et analyse de réseaux de Petri: Application aux protocoles. PhD thesis, Université de Paris 6, 1983
Berthelot, G.: Checking properties of nets using transformations. In: Rozenberg, G., (ed.) Advances in Petri Nets 1985, pp. 19–40. Berlin, Heidelberg, New York: Springer 1987
Berthomieu, B., Diaz, M.: Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. Softw. Eng.17(3), 259–273 (1991)
Buy, U., Sloan, R.: A Petri-net-based approach to real-time program analysis. In: Proc. 7th Int. Workshop on Software Specification and Design, pp. 56–60, December 1993
Buy, U., Sloan, R.H.: Automatic real-time analysis of Ada tasking programs for embedded systems.Real Time Systems (Submitted for publication), Available as Technical Report 95-1, Department of Electrical Engineering and Computer Science, University of Illinois at Chicago
Buy, U., Sloan, R.H.: Analysis of real-time programs with simple time Petri nets. In: Proc. 1994 Int. Symp. on Software Testing and Analysis, pp. 228–239, 1994
Desel, J.: Reduction and design of well-behaved concurrent systems. In: Beaten, J.C.M., Klop, J.W. (eds.) CONCUR ’90: Theories of Concurrency: Unification and Extension (Lect. Notes Comput Sci., 458, pp. 166–181) Berlin, Heidelberg, New York: Springer 1990
Duri, S., Buy, U., Devarapalli, R., Shatz, S.M.: Application and experimental evaluation of state space reduction methods for deadlock analysis in Ada. ACM Trans. Softw. Eng. Methodology3(4), 340–380 (1994)
Esparza, J., Silva, M.: Top-down synthesis of live and bounded free choice nets. In: Proc. 11th Conf. on Petri Nets, pp. 63–83, Paris, France, 1990
Estrin, G., Fenchel, R.S., Razouk, R.R., Vernon, M.K.: SARA (System ARchitects Apprentice): Modeling, analysis, and simulation support for design of concurrent systems. IEEE Trans. Softw. Eng.12(2), 293–311 (1986)
Ghezzi, C., Mandrioli, D., Morasca, S., Pezzé, M.: A general way to put time in Petri nets. In: Proc. 5th Int. Workshop on Software Specifications and Design, pp. 60–67, Pittsburgh, Pennsylvania, May 1989
Godefroid, P., Wolper, P.: Using partial orders for the efficient verification of deadlock freedom and safety properties. In: Larsen, K.G., Skou, A. (eds.) Computer-Aided Verification: 3rd Int. Conf., CAV’91 (Lect. Notes Comput. Sci., 575, pp. 332–342) Berlin, Heidelberg, New York: Springer, 1992
Haddad, S.: A reduction theory for coloured Petri nets. In: Rozenberg, G. (ed.) Advances in Petri nets, (Lect. Notes Comput. Sci., Vol. 424, pp. 209–235) Berlin, Heidelberg, New York: Springer 1990
Merlin, P., Faber, D.: Recoverability of communication protocols —implications of a theoretical study. IEEE Trans. Commun.COM-24(9), 381–404 (1976)
Murata, T.: Petri nets: Properties, analysis and applications. Proc. IEEE77(4), 541–580, 1989
Peterson, J.L.: Petri net theory and the modeling of systems. Prentice-Hall: Englewood Cliffs, NJ, 1981
Shatz, S.M., Mai, K., Black, C., Tu, S.: Design and implementation of a Petri net-based toolkit for Ada tasking analysis. IEEE Trans. Parallel Distributed Systems,1(4), 424–441 (1990)
Starke, P.H.: Reachability analysis of Petri nets using symmetries. Syst. Anal. Model. Simul.8, 293–303 (1991)
Tu, S., Shatz, S.M., Murata, T.: Applying Petri net reduction to support Ada-tasking deadlock analysis. In: Proc. 11th Int. Conf. on Distributed Computing Systems, pp. 96–103, Paris, France, 1990
Valmari, A.: A stubborn attack on state explosion. In: Clarke, E.M., Kurshan, R.P. (eds.), Computer-Aided Verification: 2nd Int. Conf., CAV’90 (Lect. Notes Comput. Sci., 531, pp. 156–165) Berlin, Heidelberg, New York: Springer 1991
Yoneda, T., Shibayama, A., Schlingloff, B.-H., Clarke, E.M.: Efficient verification of parallel real-time systems. In: Courcoubetis, C. (ed.), Computer-Aided Verification: 5th Int. Conf., CAV ’93 (Lect. Notes Comput. Sci., 697, pp. 321–332) Berlin, Heidelberg, New York: Springer 1993