Equivalence and model checking problems can be encoded into computing fixed points on dependency graphs. Dependency graphs represent causal dependencies among the nodes of the graph by means of hyper-edges. We suggest to extend the model of dependency graphs with so-called negation edges in order to increase their applicability. The graphs (as well as the verification problems) suffer from the state space explosion problem. To combat this issue, we design an on-the-fly algorithm for efficiently computing fixed points on extended dependency graphs. Our algorithm supplements previous approaches with the possibility to back-propagate, in certain scenarios, the domain value 0, in addition to the standard back-propagation of the value 1. Finally, we design a distributed version of the algorithm, implement it in our open-source tool TAPAAL, and demonstrate the efficiency of our general approach on the benchmark of Petri net models and CTL queries from the annual Model Checking Contest.
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Analysis of workflow processes with quantitative aspects like timing is of interest in numerous time-critical applications. We suggest a workflow model based on timed-arc Petri nets and study the foundational problems of soundness and strong (time-bounded) soundness. We first consider the discrete-time semantics (integer delays) and explore the decidability of the soundness problems and show, among others, that soundness is decidable for monotonic workflow nets while reachability is undecidable. For general timed-arc workflow nets soundness and strong soundness become undecidable, though we can design efficient verification algorithms for the subclass of bounded nets. We also discuss the soundness problem in the continuous-time semantics (real-number delays) and show that for nets with nonstrict guards (where the reachability question coincides for both semantics) the soundness checking problem does not in general follow the approach for the discrete semantics and different zone-based techniques are needed for introducing its decidability in the bounded case. Finally, we demonstrate the usability of our theory on the case studies of a Brake System Control Unit used in aircraft certification, the MPEG2 encoding algorithm, and a blood transfusion workflow. The implementation of the algorithms is freely available as a part of the model checker TAPAAL (www.tapaal.net).
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