Finite Model Finding for Parameterized Verification

In this paper we investigate to what extent a very simple and natural ”reachability as deducibility” approach, originating in research on formal methods for security, is applicable to the automated verification of large classes of infinite state and parameterized systems. This approach is based on modeling the reachability between (parameterized) states as deducibility between suitable encodings of states by formulas of first-order predicate logic. The verification of a safety property is reduced to the purely logical problem of finding a countermodel for a first-order formula. This task is then delegated then to generic automated finite model building procedures. In this paper we first establish the relative completeness of the finite countermodel finding method (FCM) for a class of parameterized linear arrays of finite automata. The method is shown to be at least as powerful as known methods based on monotonic abstraction and symbolic backward reachability. Further, we extend the relative completeness of the approach and show that it can solve all safety verification problems which can be solved by regular model checking.