Verification of Liveness Properties on Closed Timed-Arc Petri Nets
Verification of closed timed models by explicit state-space exploration methods is an alternative to the wide-spread symbolic techniques based on difference bound matrices (DBMs). A few experiments found in the literature confirm that for the reachability analysis of timed automata explicit techniques can compete with DBM-based algorithms, at least for situations where the constants used in the models are relatively small. To the best of our knowledge, the explicit methods have not yet been employed in the verification of liveness properties in Petri net models extended with time. We present an algorithm for liveness analysis of closed Timed-Arc Petri Nets (TAPN) extended with weights, transport arcs, inhibitor arcs and age invariants and prove its correctness. The algorithm computes optimized maximum constants for each place in the net that bound the size of the reachable state-space. We document the efficiency of the algorithm by experiments comparing its performance with the state-of-the-art model checker UPPAAL.
KeywordsReachability Analysis Liveness Property Maximum Constant Time Automaton Delay Transition
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- 1.Behrmann, G., David, A., Larsen, K.G., Hakansson, J., Petterson, P., Yi, W., Hendriks, M.: Uppaal 4.0. In: QEST 2006, pp. 125–126 (September 2006)Google Scholar
- 2.Bertolini, C., Liu, Z., Srba, J.: Verification of timed healthcare workflows using component timed-arc Petri nets. In: FHIES 2012. Springer (to appear, 2012)Google Scholar
- 10.Jacobsen, L., Jacobsen, M., Møller, M.H.: Undecidability of Coverability and Boundedness for Timed-Arc Petri Nets with Invariants. In: Proc. of MEMICS 2009, Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2009)Google Scholar
- 11.Jacobsen, L., Jacobsen, M., Møller, M.H., Srba, J.: Verification of timed-arc Petri nets. In: SOFSEM 2011, pp. 46–72 (2011)Google Scholar
- 14.Popova-zeugmann, L.: Essential states in time Petri nets. Informatik-Berichte 96 (1998)Google Scholar
- 16.Ruiz, V.V., Cuartero Gomez, F., de Frutos Escrig, D.: On non-decidability of reachability for timed-arc Petri nets. In: Proceedings of the 8th International Workshop on Petri Net and Performance Models (PNPM 1999), pp. 188–196 (1999)Google Scholar