Testing Undecidability of the Reachability in Petri Nets with the Help of 10th Hilbert Problem
The 10th Hilbert problem is used as a test for undecidability of reachability problem in some classes of Petri Nets, such as self-modifying nets, nets with priorities and nets with inhibitor arcs. Common method is proposed in which implementing in a weak sense the multiplication in a given class of Petri nets including PT-nets is sufficient for such undecidability.
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- DFSch 98.C. Dufourd, A. Finkel, Ph. Schnoebelen, Reset nets: between decidability and undecidability, Proceedings ICALP 98, Aalborg (1998)Google Scholar
- Hack 74.M. Hack, Decidability question for Petri nets, PhD thesis, Department of Electrical Engineering, MIT 1974.Google Scholar
- Hack 76.
- Kindler 98.E. Kindler, Private communication.Google Scholar
- Kosaraju 82.S.R. Kosaraju, Decidability of Reachability in Vector Addition Systems, In Proc. of the 14th Annual ACM Symp. on Theory of Computing, San Francisco, May 5-7, 1982, pages 267–281 (1982)Google Scholar
- Matijasevich 70.Y. Matijasevich, Enumerable sets are Diophantine(in Russian), Dokl. Akad. Nauk SSSR, 191, pp 279–282 (1970). Translation in: Soviet Math. Doklady, 12 pp 249-254, (1971)Google Scholar
- Mayr 81.E. Mayr, An algorithm for the general Petri net reachability problem. Proceedings of the 13th Ann. ACM Symposium on Theory of Computing, May 11-13, 1981 (Milwaukee, WI), pp. 238–246. Also: SIAM Journal on Computing 13, 3, pp. 441-460.Google Scholar
- Tarlecki 83.A. Tarlecki, An obvious observation on functions computable by Petri Nets, SIG Petri Nets and Related Models, Newsletter 13 (February 1983)Google Scholar