Petri Nets with Time and Cost

We consider timed Petri nets, i.e., unbounded Petri nets where each token carries a real-valued clock. Transition arcs are labeled with time intervals, which specify constraints on the ages of tokens. Our cost model assigns token storage costs per time unit to places, and firing costs to transitions. We study the cost to reach a given control-state. In general, a cost-optimal run may not exist. However,we show that the infimum of the costs is computable.

[1]  C. Petri.  Kommunikation mit Automaten , 1962 .

[2]  Rémi Bonnet.  The Reachability Problem for Vector Addition System with One Zero-Test , 2011, MFCS.

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

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

[5]  Kim G. Larsen,et al.  Optimal Strategies in Priced Timed Game Automata , 2004, FSTTCS.

[6]  Serge Haddad,et al.  Comparison of Different Semantics for Time Petri Nets , 2005, ATVA.

[7]  Parosh Aziz Abdulla,et al.  Model checking of systems with many identical timed processes , 2003, Theor. Comput. Sci..

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

[9]  Parosh Aziz Abdulla,et al.  Computing Optimal Coverability Costs in Priced Timed Petri Nets , 2011, 2011 IEEE 26th Annual Symposium on Logic in Computer Science.

[10]  James L. Peterson,et al.  Petri Nets , 1977, CSUR.

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

[12]  Marc Boyer,et al.  Time Petri Nets , 2010 .

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

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

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