On Symmetries and Spotlights - Verifying Parameterised Systems

Parameterised model checking is concerned with verifying properties of arbitrary numbers of homogeneous processes composed in parallel. The problem is known to be undecidable in general. Nevertheless, a number of approaches have developed verification techniques for certain classes of parameterised systems. Here, we present an approach combining symmetry arguments with spotlight abstractions. The technique determines (the size of) a particular instantiation of the parameterised system from the given temporal logic formula, and feds this into an abstracting model checker. The degree of abstraction with respect to processes occurring during model checking determines whether the obtained result is also valid for all other instantiations. This enables us to prove safety as well as liveness properties (specified in full CTL) of parameterised systems on very small instantiations.