Automatic Non-Interference Lemmas for Parameterized Model Checking

Parameterized

model

checking
refers to any method that extends traditional, finite-state model checking to handle systems with an arbitrary number of processes. One popular approach to this problem uses abstraction and so-called
guard

strengthening
. Here a small number of processes remain intact, while the rest are abstracted away. This initially causes counter-examples, but the user can write
non-interference

lemmas
, which eliminate spurious behavior by the abstracted processes. The technique is sound in that if the user writes a lemma that is not invariant, the proof will never succeed. Though the non-interference lemmas are typically much simpler than writing a full inductive invariant, there is still a non-trivial amount of human insight needed to analysis counter-examples and concoct the lemmas. In our work, we show how the process of inferring appropriate non-interference lemmas can be automated. Our approach is based on a very general theory that simply assumes a
Galois

connection
between the concrete and abstract systems. Effectively, we start with the non-interference conjecture
false
, and iteratively weaken it until it is provable using the Galois connection. This produces the
strongest
non-interference lemma provable in the Galois connection. Hence, if the approach fails to prove the property, then no human lemma would help, since it is the strongest possible lemma. We instantiate this theory to a class of symmetric parameterized systems, and show how BDDs can be used to perform all involved computations. We also show how BDD-blow up that can arise when concretizing can be mitigated by using a sound over-approximation. We successfully applied the resulting tool to three parameterized verification benchmarks: the GERMAN protocol with data path, the GERMAN2004 protocol, and the FLASH protocol. To our knowledge, this is the first time automatic parameterized model checking has been done on GERMAN2004.