Efficient model-checking of weighted CTL with upper-bound constraints

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”.