Reset Nets Between Decidability and Undecidability

We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decidability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separations between seemingly related problems. Our main theorem is the very surprising fact that boundedness is undecidable for Petri nets with Reset arcs.

[1]  Philippe Schnoebelen,et al.  Fundamental Structures in Well-Structured Infinite Transition Systems , 1998, LATIN.

[2]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .

[3]  Luciano Lavagno,et al.  Coupling Asynchrony and Interrupts: Place Chart Nets , 1997, ICATPN.

[4]  Alain Finkel,et al.  Reduction and covering of infinite reachability trees , 1990, Inf. Comput..

[5]  Gianfranco Ciardo,et al.  Petri Nets with Marking-Dependent Ar Cardinality: Properties and Analysis , 1994, Application and Theory of Petri Nets.

[6]  Richard M. Karp,et al.  Parallel Program Schemata , 1969, J. Comput. Syst. Sci..

[7]  Jonathan Billington,et al.  Extensions to coloured Petri nets and their application to protocols , 1991 .

[8]  Michel Hack,et al.  Decidability Questions for Petri Nets , 1975, Outstanding Dissertations in the Computer Sciences.

[9]  Charles Rackoff,et al.  The Covering and Boundedness Problems for Vector Addition Systems , 1978, Theor. Comput. Sci..

[10]  Tadao Kasami,et al.  Some Decision Problems Related to the Reachability Problem for Petri Nets , 1976, Theor. Comput. Sci..

[11]  Rüdiger Valk.  On the Computational Power of Extended Petri Nets , 1978, MFCS.

[12]  Parosh Aziz Abdulla,et al.  General decidability theorems for infinite-state systems , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[13]  Rüdiger Valk.  Self-Modifying Nets, a Natural Extension of Petri Nets , 1978, ICALP.

[14]  Wolfgang Reisig,et al.  Application and Theory of Petri Nets , 1982, Informatik-Fachberichte.

[15]  Walter Vogler,et al.  Partial order semantics and read arcs , 1997, Theor. Comput. Sci..

[16]  Søren Christensen,et al.  A General Systematic Approach to Arc Extensions for Coloured Petri Nets , 1994, Application and Theory of Petri Nets.