Verifying Universal Properties of Parameterized Networks

We present a method for verifying universal properties of fair parameterized networks of finite processes, that is, properties of the form ∀p1...pn: ψ, where ψ is a quantifier-free LTL formula. The starting point of our verification method is an encoding of the infinite family of networks by a single fair transition system whose variables are set (2nd-order) variables and transitions are described in WS1S, such a system is called a WS1S transition system. We abstract the WS1S system into a finite state system that can be model-checked. We present a generic abstraction relation for verifying universal properties as well as an algorithm for computing an abstract system. Since, the abstract system may contain infinite computations that have no corresponding fair computations at the concrete level, the verification of progress property often fails. Therefore, we present methods that allow to synthesize fairness conditions from the parameterized network and discuss under which conditions and how to lift fairness conditions of this network to fairness conditions on the abstract system. We implemented our methods in a tool, called PAX, and applied it to several examples.