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A Distributed Fixed-Point Algorithm for Extended Dependency Graphs

Dalsgaard A. E., Enevoldsen S., Fogh P., Jensen L. S., Jensen P. G., Jepsen T. S., Kaufmann I., Larsen K. G., Nielsen S. M., Olesen M. C., Pastva S., Srba J.

Fundamenta Informaticae

2018

Vol. 161, nr 4

351--381

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.