Some consequences of the decidability of the reachability problem for Petri nets
The aim of this article is to explain and elucidate Mayr's and Kosaraju's proof of the decidability of reachability in Petri nets. We introduce the new notion of precovering graphs which allows to suppress technical steps and makes the result clearer. We obtain a new structure on Petri nets: the perfect marked graph-transition sequences which generalises, in the case we add a final marking to the Petri net, the covering graph. We deduce from this structure new results in Petri net language theory.
Unable to display preview. Download preview PDF.
- N. Dershowitz, Z. Manna, Proving termination with multiset ordering, Comm. ACM, August 79, Volume 22, Nr 8.Google Scholar
- J.Hopcroft, J.J. Pansiot, On the reachability problem for 5-dimensional vector addition systems, Theoret. Comp. Sci., 1978, 135–159.Google Scholar
- M. Jantzen, On the hierarchy of Petri net languages, RAIRO Vol 13 no1, 1979, 19–30.Google Scholar
- R.M. Karp, R.E. Miller, Parallel program schemata, J. Comput. Sci. 3 (May 1969) 147–195.Google Scholar
- S.R. Kosaraju, Decidability of reachability in vector addition systems, Proc. 14 th ann. ACM STOC, 1982, 267–281.Google Scholar
- J.L. Lambert, A structure to decide reachability in Petri net, to appear in Theoret. Comp. Sci.Google Scholar
- J.L. Lambert, Finding a partial solution to a linear system of equations in positive integer, Comput. Math. Applic. Vol. 15, No3, pp 209–212, 1988.Google Scholar
- E. Mayr, An algorithm for the general Petri net reachability problem, SIAM, J. Comput., Vol 13 No3, 1984, 441–460. AndGoogle Scholar
- E.Mayr, An algorithm for the general Petri net reachability problem, Proc. 13 th ann. ACM STOC, 1981, 238–246.Google Scholar
- H. Muller, The reachability problem for VAS, Advances in Petri nets 1984, LNCS 188, 376–391Google Scholar
- M. Parigot, E. Pelz, A logical formalism for the study of the finite behaviour of Petri nets, Advances in Petri net 1985, LNCS 222, 346–361Google Scholar
- C.A. Petri, Kommunikation mit Automaten, Institut für Instrumentelle Mathematik (Bonn), Schriften des IMM Nr 2, 1962.Google Scholar