The problem of invariant checking in parametric systems – which are required to operate correctly regardless of the number and connections of their components – is gaining increasing importance in various sectors, such as communication protocols and control software. Such systems are typically modeled using quantified formulae, describing the behaviour of an unbounded number of (identical) components, and their automatic verification often relies on the use of decidable fragments of first-order logic in order to effectively deal with the challenges of quantified reasoning.In this paper, we propose a fully automatic technique for invariant checking of parametric systems which does not rely on quantified reasoning. Parametric systems are modeled with array-based transition systems, and our method iteratively constructs a quantifier-free abstraction by analyzing, with SMT-based invariant checking algorithms for non-parametric systems, increasingly-larger finite instances of the parametric system. Depending on the verification result in the concrete instance, the abstraction is automatically refined by leveraging canditate lemmas from inductive invariants, or by discarding previously computed lemmas.We implemented the method using a quantifier-free SMT-based IC3 as underlying verification engine. Our experimental evaluation demonstrates that the approach is competitive with the state of the art, solving several benchmarks that are out of reach for other tools.
We consider the problem of invariant checking for transition systems using SMT and quantified variables ranging over finite but unbounded domains. We propose a general approach, obtained by combining two ingredients: exploration of a finite instance, to obtain candidate inductive invariants, and instantiation-based techniques to discharge quantified queries. A thorough experimental evaluation on a wide range of benchmarks demonstrates the generality and effectiveness of our approach. Our algorithm is the first capable of approaching in a uniform way such a large variety of models.
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