A necessary and sufficient condition for the liveness of normal nets

Computer Journal

Volumn 54, Issue 1, 2011, Pages 157-163

  Liu, GuanJun ^a   Jiang, ChangJun ^a   Chao, Daniel Y ^b  

^a TONGJI UNIVERSITY   (China)

^b NATIONAL CHENGCHI UNIVERSITY   (Taiwan)

Author keywords

liveness; normal nets; Petri nets; siphons; structural repetitiveness; weakly persistent nets

Indexed keywords

INITIAL MARKING; LIVENESS; MINIMAL SIPHONS; NET STRUCTURES; NORMAL NETS; STRUCTURAL REPETITIVENESS; SUFFICIENT CONDITIONS; WEAKLY PERSISTENT NETS;

GRAPH THEORY; MATHEMATICAL TECHNIQUES; PETRI NETS;

SIPHONS;

EID: 78650867909     PISSN: 00104620     EISSN: 14602067     Source Type: Journal    
DOI: 10.1093/comjnl/bxp118     Document Type: Article

References (23)

1. Yamasaki, H. (1981) On weak persistency of Petri nets. Inform. Process. Lett., 13, 94-97.
2. Yamasaki, H. (1984) Normal Petri nets. Theor. Comput. Sci., 31, 307-315.
3. Hiraishi, K. and Ichikawa,A. (1992) On structural conditions for weak persistency and semilinearity of Petri nets. Theor. Comput. Sci., 93, 185-199.
4. Ichikawa, A. and Hiraishi, K. (1987) Analysis and control of discrete event systems represented by Petri nets. Lect. Notes Control Inf. Sci., 103, 115-134.
5. Howell, R.R., Rosier, L.E. and Yen, H.C. (1993) Normal and sinkless Petri nets. J. Comput. Syst. Sci., 46, 1-26.
6. Landweber, L.H. and Robertson, E.L. (1978) Properties of conflict-free and persistent Petri nets. J. ACM, 25, 352-364.
7. Darondeau, Ph. (2005) Equality of languages coincides with isomorphism of reachable state graphs for bounded and persistent Petri nets. Inform. Process. Lett., 94, 241-245.
8. Best, E. and Darondeau, Ph. (2008) Decomposition theorems for bounded persistent Petri nets. Lect. Notes Comput. Sci., 5062, 33-51.
9. Desel, J. and Esparza, J. (1995) Free Choice Petri Nets. Cambridge University Press, London.
10. Baccelli, F., Foss, S. and Gaujal, B. (1996) Free-choice Petri nets: an algebraic approach. IEEE Trans. Automat. Contr., 41, 1751-1778.
11. Iordache, M.V. and Antsaklis, P.J. (2006) Supervisory Control of Concurrent Systems: A Petri Net Structural Approach. Springer, Berlin.
12. Li, Z.W. and Zhou, M.C. (2009) Deadlock Resolution in Automated Manufacturing Systems: A Novel Petri Net Approach. Springer, NewYork.
13. Best, E. and Shields, M.W. (1983) Some equivalence results on free choice nets and simple nets, and on the periodicity of live free choice nets. Lect. Notes Comput. Sci., 159, 141-151.
14. Chu, F. and Xie, X.L. (1997) Deadlock analysis of Petri nets using siphons and mathematical programming. IEEE Trans. Robot. Automat., 13, 793-804.
15. Jiao, L., Chueng, T.Y. and Lu, W.M. (2004) On liveness and boundness of symmetric choice nets. Theor. Comput. Sci., 311, 165-197.
16. Murata, T. (1989) Petri nets: properties, analysis, and applications. Proc. IEEE, 77, 541-580.
17. Silva, M., Teruel, E. and Colom, J. (1996) Linear algebraic and linear programming techniques for the analysis of place/transition net systems. Lect. Notes Comput. Sci., 1491, 309-373.
18. Liu, G.J. and Jiang, C.J. (2009) Incidence matrix based methods for computing repetitive vectors and siphons of Petri net. J. Inf. Sci. Eng., 25, 121-136.
19. Liu, G.J. and Jiang, C.J. (2009) On conditions for the liveness of weakly persistent nets. Inform. Process. Lett., 109, 967-970.
20. Hack, M. (1976) Decidability questions for Petri nets. PhD Thesis, Massachusetts Institute of Technology.
21. Lipton, R.J. (1976) The Reachability Problem Requires Exponential Space. Research Report 62, Department of Computer Science,Yale University.
22. Peterson, J.L. (1981) Petri Net Theory and the Modeling of Systems. Prentice-Hall, Englewood Cliffs.
23. Wu, Z.H. (2006) An Introduction to Petri Nets. China Machine Press, Beijing (in Chinese).