We aim at measuring the influence of the nondeterministic choices of a part
of a system on its ability to satisfy a specification. For this purpose, we
apply the concept of Shapley values to verification as a means to evaluate how
important a part of a system is. The importance of a component is measured by
giving its control to an adversary, alone or along with other components, and
testing whether the system can still fulfill the specification. We study this
idea in the framework of model-checking with various classical types of
linear-time specification, and propose several ways to transpose it to
branching ones. We also provide tight complexity bounds in almost every case.Comment: 22 pages, 12 figure
