Linear time analysis of properties of conflict-free and general Petri nets

Theoretical Computer Science

Volumn 412, Issue 4-5, 2011, Pages 320-338

  Alimonti, Paola ^a   Feuerstein, Esteban ^b   Laura, Luigi ^a   Nanni, Umberto ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSIDAD DE BUENOS AIRES   (Argentina)

Author keywords

Boundedness; Conflict free Petri nets; Coverability; Directed hypergraphs; Incremental algorithms; Liveness; Marked graphs; Petri nets

Indexed keywords

BOUNDEDNESS; CONFLICT FREE; COVERABILITY; DIRECTED HYPERGRAPHS; INCREMENTAL ALGORITHM; LIVENESS; MARKED GRAPHS;

ALGORITHMS; GRAPH THEORY; PETRI NETS; TEACHING;

PROBLEM SOLVING;

EID: 78650815260     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2010.09.030     Document Type: Article

References (39)

1. A.V. Aho, J.E. Hopcroft, and J.D. Ullman The Design and Analysis of Computer Algorithms 1974 Addison-Wesley
2. G. Ausiello, A. D'Atri, and D. Sacc Graph algorithms for functional dependency manipulation Journal of the ACM 30 1983 752 766
3. G. Ausiello, P.G. Franciosa, and D. Frigioni Partially dynamic maintenance of minimum weight hyperpaths Journal of Discrete Algorithms 3 1 2005 27 46
4. G. Ausiello, and G.F. Italiano Online algorithms for polynomially solvable satisfiability problems Journal of Logic Programming 10 1991 69 90
5. G. Ausiello, G.F. Italiano, and U. Nanni Dynamic maintenance of directed hypergraphs Theoretical Computer Science 72 23 1990 97 117
6. C. Berge Graphs and Hypergraphs 1973 North Holland Amsterdam
7. E. Best A note on persistent Petri nets Concurrency, Graphs and Models: Essays Dedicated to Ugo Montanari on the Occasion of His 65th Birthday Lecture Notes in Computer Science vol. 5065 2008 Springer-Verlag 427 438
8. H. Boley Directed recursive labelnode hypergraphs: a new representation language Artificial Intelligence 9 1977 49 85
9. A. Cheng, J. Esparza, and J. Palsberg Complexity results for 1-safe nets Theoretical Computer Science 147 12 1995 117 136
10. F. Chu, and X. Xie Deadlock analysis of Petri nets using siphons and mathematical programming IEEE Transactions on Robotics and Automation 13 6 1997 793 804
11. F. Commoner, A.W. Holt, S. Even, and A. Pnueli Marked directed graphs Journal of Computer and System Sciences 5 5 1971 511 523
12. T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein Introduction to Algorithms second ed. 2001 MIT Press
13. S. Crespi-Reghizzi, and D. Mandrioli A decidability theorem for a class of vector additions systems Information Processing Letters 3 3 1975 78 80
14. J. Esparza, and M. Nielsen Decidability issues for Petri nets a survey Bulletin EATCS 52 1994 245 262
15. J. Esparza, and M. Silva A polynomial-time algorithm to decide liveness of bounded free-choice nets Theoretical Computer Science 102 1 1992 185 205
16. G. Gallo, G. Longo, S. Nguyen, S. Pallottino, Directed Hypergraphs and Applications, Technical Report 3/90, Dip. di Informatica, Univ. of Pisa, Italy, January 1990.
17. C. Ghezzi, D. Mandrioli, S. Morasca, and M. Pezz A unified high-level Petri net formalism for time-critical systems IEEE Transactions on Software Engineering 17 2 1991 160 172
18. M.H.T. Hack, The recursive equivalence of the reachability problem and the liveness problem for Petri nets and vector addition systems, in: 15th Annual Symposium on Switching and Automata Theory, 1974, pp. 156164.
19. R. Howell, and L. Rosier Problems concerning fairness and temporal logic for conflict-free Petri nets Theoretical Computer Science 64 3 1989 305 329
20. R. Howell, L. Rosier, and H. Yen An O (n 1.5 ) algorithm to decide boundedness for conflict-free vector replacement system Information Processing Letters 25 1 1987 27 33
21. R. Howell, L. Rosier, and H. Yen A taxonomy of fairness and temporal logic problems for Petri nets Theoretical Computer Science 82 2 1991 341 372
22. M.D. Jeng, and X. Xie Analysis of modularly composed nets by siphons IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 29 4 1999 399 406
23. N.D. Jones, L.H. Landweber, and Y.E. Lien Complexity of some problem in Petri nets Theoretical Computer Science 4 3 1977 277 299
24. R.M. Karp, and R. Miller Parallel program schemata Journal of Computer and System Sciences 3 2 1969 147 195
25. R. Keller A fundamental theorem of asynchronous parallel computation Tse-yun Feng, Parallel Processing Lecture Notes in Computer Science vol. 24 1975 Springer-Verlag 102 112
26. L. Landweber, and E. Robertson Properties of conflict-free and persistent Petri nets Journal of the ACM 25 3 1978 352 364
27. R. Lipton, The reachability problem requires exponential space, Technical Report 62, Department of Computer Science, Yale Universitéy, 1976.
28. E. Mayr An algorithm for the general Petri net reachability problem SIAM Journal on Computing 13 3 1984 441 459
29. T. Murata, Petri nets: properties, analysis and applications, in: Proceedings of the IEEE, 1989, pp. 541580.
30. J.L. Peterson Petri nets Computing Surveys 9 3 1977 223 252
31. C.A. Petri, Communication with automata, Technical Report Supplement 1 to Tech. Report RADC-TR-65-377, 1966, Rome Air Development Center (US Air Force), 1962. Original in German: Kommunikation mit Automaten, Ph.D. Thesis, Univ. of Bonn, 1962.
32. L. Piroddi, R. Cordone, and I. Fumagalli Combined siphon and marking generation for deadlock prevention in Petri nets IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 39 3 2009 650 661
33. C. Rackoff The covering and boundedness problems for vector addition systems Theoretical Computer Science 6 2 1978 223 231
34. W. Reisig Petri Nets, An Introduction ETACS Monographs Theoretical Computer Science 1985 Springer-Verlag
35. L. Roditty, and U. Zwick A fully dynamic reachability algorithm for directed graphs with an almost linear update time STOC'04: Proceedings of the Thirty-sixth Annual ACM Symposium on Theory of Computing Chicago, IL, June 1315, 2004 2004 ACM 184 191
36. R.E. Tarjan Efficiency of a good but not linear set union algorithm Journal of the ACM 22 2 1975 215 225
37. M. Thakur, and R. Tripathi Linear connectivity problems in directed hypergraphs Theoretical Computer Science 410 2729 2009 2592 2618
38. H. Yen A unified approach for deciding the existence of certain Petri nets paths Information and Computation 96 1 1992 119 137
39. M.C. Zhou, and F. DiCesare Parallel and sequential mutual exclusions for Petri net modeling for manufacturing systems with shared resources IEEE Transactions on Robotics and Automation 7 4 1991 515 527