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Abstract

We present a symbolic extension of dependency graphs by Liu and Smolka in to model-check weighted Kripke structures against the computation tree logic with upper-bound weight constraints. Our extension introduces a new type of edges into dependency graphs and lifts the computation of fixed-points from boolean domain to nonnegative integers to cope with the weights. We present both global and local algorithms for the fixed-point computation on symbolic dependency graphs and argue for the advantages of our approach compared to the direct encoding of the model-checking problem into dependency graphs. We implement all algorithms in a publicly available tool and evaluate them on several experiments. The principal conclusion is that our local algorithm is the most efficient one with an order of magnitude improvement for model checking problems with a high number of “witnesses”.

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Notes

  1. Exponential in the encoding of the weights in the model and the formula.

  2. A blocking WKS can be turned into a nonblocking one by introducing a new state with no atomic propositions, zero-weight self-loop and with zero-weight transitions from all blocking states into this newly introduced state.

  3. At line 12 we added the assignment \(D(u) = \{ e \}\); the original algorithm sets the dependency set to empty here, leading to an incorrect propagation.

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Acknowledgments

We thank the anonymous reviewers for their useful comments and suggestions. The research leading to these results has received funding from the EU Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 601148 (CASSTING).

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Correspondence to Jiří Srba.

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Jensen, J.F., Larsen, K.G., Srba, J. et al. Efficient model-checking of weighted CTL with upper-bound constraints. Int J Softw Tools Technol Transfer 18, 409–426 (2016). https://doi.org/10.1007/s10009-014-0359-5

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