Liveness and Acceleration in Parameterized Verification

The paper considers the problem of uniform veriication of parameterized systems by symbolic model checking, using formulas in fs1s (a syntactic variant of the 2nd order logic ws1s) for the symbolic representation of sets of states. The technical diiculty addressed in this work is that, in many cases, standard model-checking computations fail to converge. Using the tool tlvP ], we formulated a general approach to the acceleration of the transition relations, allowing an unbounded number of diierent processes to change their local state (or interact with their neighbor) in a single step. We demonstrate that this acceleration process solves the diiculty and enables an eecient symbolic model-checking of many parameterized systems such as mutual-exclusion and token-passing protocols for any value of N, the parameter specifying the size of the system. Most previous approaches to the uniform veriication of parameterized systems, only considered safety properties of such systems. In this paper , we present an approach to the veriication of liveness properties and demonstrate its application to prove accessibility properties of the considered protocols.