Minimal Cost Reachability/Coverability in Priced Timed Petri Nets

We extend discrete-timed Petri nets with a cost model that assigns token storage costs to places and firing costs to transitions, and study the minimal cost reachability/coverability problem. We show that the minimal costs are computable if all storage/transition costs are non-negative, while even the question of zero-cost coverability is undecidable in the case of general integer costs.

[1]  Klaus Reinhardt,et al.  Reachability in Petri Nets with Inhibitor Arcs , 2008, RP.

[2]  L. Dickson.  Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors , 1913 .

[3]  Robin Milner.  The Flux of Interaction , 2001, ICATPN.

[4]  David de Frutos-Escrig,et al.  On non-decidability of reachability for timed-arc Petri nets , 1999, PNPM.

[5]  RaskinJean-François,et al.  On the optimal reachability problem of weighted timed automata , 2007 .

[6]  Mogens Nielsen,et al.  Application and Theory of Petri Nets 2000: 21st International Conference, ICATPN 2000 Aarhus, Denmark, June 26–30, 2000 Proceedings , 2000, ICATPN.

[7]  Rüdiger Valk,et al.  The residue of vector sets with applications to decidability problems in Petri nets , 1985, Acta Informatica.

[8]  Kim G. Larsen,et al.  As Cheap as Possible: Efficient Cost-Optimal Reachability for Priced Timed Automata , 2001, CAV.

[9]  Parosh Aziz Abdulla,et al.  Timed Petri Nets and BQOs , 2001, ICATPN.

[10]  Rami R. Razouk,et al.  Performance Analysis Using Timed Petri Nets , 1984, PSTV.

[11]  George J. Pappas,et al.  Optimal Paths in Weighted Timed Automata , 2001, HSCC.

[12]  Ernst W. Mayr.  An Algorithm for the General Petri Net Reachability Problem , 1984, SIAM J. Comput..

[13]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[14]  Petr Jancar,et al.  Decidability of a Temporal Logic Problem for Petri Nets , 1990, Theor. Comput. Sci..

[15]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[16]  Véronique Bruyère,et al.  On the optimal reachability problem of weighted timed automata , 2007, Formal Methods Syst. Des..

[17]  P. Merlin,et al.  Recoverability of Communication Protocols - Implications of a Theoretical Study , 1976, IEEE Transactions on Communications.

[18]  Carlo Ghezzi,et al.  A Unified High-Level Petri Net Formalism for Time-Critical Systems , 1991, IEEE Trans. Software Eng..

[19]  David de Frutos-Escrig,et al.  Decidability of Properties of Timed-Arc Petri Nets , 2000, ICATPN.

[20]  M. Diaz,et al.  Modeling and Verification of Time Dependent Systems Using Time Petri Nets , 1991, IEEE Trans. Software Eng..