Computational complexity of the place/transition-net symmetry reduction method

Journal of Universal Computer Science

Volumn 7, Issue 4, 2001, Pages 307-326

  Junttila, Tommi A ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Computational complexity; Petri nets; Symmetry

Indexed keywords

EID: 33947261169     PISSN: 0958695X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. [Babai 1994] Babai, L.: "Automorphism groups, isomorphism, reconstruction"; Technical Report TR-94-10, University of Chicago, Department of Computer Science (1994).
2. Also as chapter 27 of the "Handbook of Combinatorics", North-Holland (1995).
3. [Babai and Luks 1983] Babai, L., Luks, E. M.: "Canonical labeling of graphs"; Proc. Fifteenth Annual ACM Symposium on Theory of Computing, ACM (1983), 171-183.
4. [Blass and Gurevich 1984] Blass, A., Gurevich, Y.: "Equivalence relations, invariants, and normal forms"; SIAM Journal on Computing, 13, 4 (1984), 682-689.
5. [Boppana et al. 1987] Boppana, R. B., Hastad, J., Zachos, S.: "Does co-NP have short interactive proofs?" Information Processing Letters, 25, 2 (1987), 127-132.
6. [Butler 1991] Butler, G.: "Fundamental Algorithms for Permutation groups"; volume 559 of Lecture Notes in Computer Science, Springer-Verlag, Berlin (1991).
7. [Clarke et al. 1998] Clarke, E. M., Emerson, E. A., Jha, S., Sistla, A. P.: "Symmetry reductions in model checking"; in "Computer Aided Verification (CAV'98)", eds. Hu, A. J. and Vardi, M. Y., volume 1427 of Lecture Notes in Computer Science, Springer, Berlin (1998), 147-158.
8. [Clarke et al. 1996] Clarke, E, M., Enders, R., Filkorn, T., Jha, S.: "Exploiting symmetry in temporal logic model checking"; Formal Methods in System Design, 9, 1/2 (1996), 77-104.
9. [Emerson and Sistla 1996] Emerson, E.A., Sistla, A.P.: "Symmetry and model checking"; Formal Methods in System Design, 9, 1/2 (1996), 105-131.
10. [Esparza 1998] Esparza, J.: "Decidability and complexity of Petri net problems -an introduction"; in "Lectures on Petri Nets I: Basic Models", Reisig, W., Rozenberg, G., eds., volume 1491 of Lecture Notes in Computer Science, Springer (1998), 374-428.
11. [Finkel 1990] Finkel, A.: "The minimal coverability graph for Petri nets"; Proc. 11th Internation Conference on Application and Theory of Petri Nets (1990), 1-21.
12. [Furst et al. 1980] Furst, M., Hopcroft, J., Luks, E.: "Polynomial-time algorithms for permutation groups"; Proc. 21st Annual Symposium on Foundations of Computer Science, IEEE (1980), 36-41.
13. [Garey and Johnson 1979] Garey, M. R., Johnson, D. S.: "Computers and Intractability: A Guide to the Theory of NP-Completeness"; W. H. Freeman and Company, San Francisco (1979).
14. [Genrich 1991] Genrich, H. J.: "Predicate/transition nets"; in "High-level Petri Nets; Theory and Application", Jensen, K., Rozenberg, G., eds., Springer-Verlag (1991), 3-43.
15. [Goldreich et al. 1986] Goldreich, O., Micali, S., Wigderson, A.: "Proofs that yield nothing but their validity and a methodology of cryptographic protocol design"; Proc. 27th Annual Symposium on Foundations of Computer Science, IEEE (1986), 174-187.
16. [Gyuris and Sistla 1999] Gyuris, V., Sistla, A. P.: "On-the-fly model checking under fairness that exploits symmetry"; Formal Methods in System Design, 15, 3 (1999), 217-238.
17. [Huber et al. 1984] Huber, P., Jensen, A. M., Jepsen, L. O., Jensen, K.: "Towards reachability trees for high-level Petri nets"; in "Advances in Petri Nets 1984", Rozenberg, G., ed., volume 188 of Lecture Notes in Computer Science Springer-Verlag (1985), 215-233.
18. [Huber et al. 1991] Huber, P., Jensen, A. M., Jepsen, L. O., Jensen, K.: "Reachability trees for high-level Petri nets"; in "High-level Petri Nets; Theory and Application", Jensen, K., Rozenberg, G., eds., Springer-Verlag (1991), 319-350.
19. [Ip and Dill 1996] Ip, C. N. and Dill, D. L.: "Better verification through symmetry"; Formal Methods in System Design, 9, 1/2 (1996), 41-76.
20. [Jensen 1995] Jensen, K.: "Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use: Volume 2, Analysis Methods"; Monographs in Theoretical Computer Science, Springer-Verlag (1995).
21. [Jensen 1996] Jensen, K.: "Condensed state spaces for symmetrical coloured Petri nets"; Formal Methods in System Design, 9, 1/2 (1996), 7-40.
22. [Jerrum 1986] Jerrum, M.: "A Compact Representation for Permutation Groups"; Journal of Algorithms, 7, 1 (1986), 60-78.
23. [Junttila 1999] Junttila, T.: "Detecting and exploiting data type symmetries of algebraic system nets during reachability analysis"; Research Report A57, Helsinki University of Technology, Laboratory for Theoretical Computer Science, Espoo, Finland (1999).
24. [Karp and Miller 1969] Karp, R. M., Miller, R. E.: "Parallel Program Schemata"; Journal of Computer and System Sciences, 3, 2 (1969). 147-195.
25. [Köbler et al. 1993] Köbler, J., Schöning, U., Torán, J.: "The Graph Isomorphism Problem: Its Structural Complexity"; Progress in Theoretical Computer Science, Birkhäuser, Boston (1993).
26. [Kreher and Stinson 1999] Kreher, D. L., Stinson, D. R.: "Combinatorial Algorithms: Generation, Enumeration and Search"; CRC Press, Boca Raton, Florida (1999).
27. [Krentel 1988] Krentel, M. W.: "The complexity of optimization problems"; Journal of Computer and System Sciences, 36, 3 (1988). 490-509.
28. [Luks 1993] Luks, E. M.: "Permutation groups and polynomial-time computation"; Technical Report CIS 93-01, Department of Computer and Information Science, University of Oregon (1993).
29. Also published in "Groups and Computation", L. Finkelstein and W. M. Kantor, Eds. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, DIMACS (1993).
30. [McKay 1990] McKay, B. D.: "Nauty user's guide (version 1.5)"; Technical Report TR-CS-90-02, Computer Science Department, Australian National University (1990).
31. [Miller 1979] Miller, G. L.: "Graph isomorphism, general remarks"; Journal of Computer and System Sciences, 18, 2 (1979), 128-142.
32. [Papadimitriou 1994] Papadimitriou, C. H.: "Computational Complexity". Addison-Wesley, Reading, Massachusetts (1994).
33. [Petrucci 1990] Petrucci, L.: "Combining Finkel's and Jensen's reduction techniques to build covering trees for coloured nets"; Petri Net Newsletter, 36 (1990), 32-36.
34. [Schmidt 1997] Schmidt, K.: "How to calculate symmetries of Petri nets"; Technical Report MATH-AL-8-1997, Technische Universität Dresden, Germany (1997).
35. [Schmidt 2000a] Schmidt, K.: "How to calculate symmetries of Petri nets"; Acta Informatica, 36, 7 (2000), 545-590.
36. [Schmidt 2000b] Schmidt, K.: "Integrating low level symmetries into reachability analysis"; in "Tools and Algorithms for the Construction and Analysis of Systems; 6th International Conference, TACAS 2000", Graf, S., Schwartzbach, M., eds., volume 1785 of Lecture Notes in Computer Science, Springer (2000), 315-330.
37. [Schmidt and Starke 1991] Schmidt, K., Starke, P. H.: "An algorithm to compute the symmetries of Petri nets"; Petri Net Newsletter, 40 (1991), 25-30.
38. [Starke 1991] Starke, P. H.: "Reachability analysis of Petri nets using symmetries"; Systems Analysis Modelling Simulation, 8, 4/5 (1991), 293-303.
39. [Valmari 1998] Valmari, A.: "The state explosion problem"; in "Lectures on Petri Nets I: Basic Models", Reisig, W., Rozenberg, G., eds., volume 1491 of Lecture Notes in Computer Science, Springer (1998), 429-528.