Universal Invariant Checking of Parametric Systems with Quantifier-free SMT Reasoning

Abstract

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.

Bounded Model Checking of Max-Plus Linear Systems via Predicate Abstractions

“…As future work, we plan to investigate the case of models with reducible matrices and unbounded transients. Furthermore, we will generalize the approach for parametric MPL, where the matrices may contain symbolic expressions, by considering the use of parametric model checking techniques [61].…”

Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays

“…We believe that this issue can be circumvented in an automated fashion with future work. In fact, an approach introduced since the conference version [MIG + 21] of this paper uses prophecy variables with a different refinement loop for verifying parameterized protocols, which cannot be handled by our technique due to this limitation [CGR21].…”

The VMT-LIB Language and Tools

“…Recently, the language has been adopted also by the AVR [11] model checker. VMT-LIB is also the native language of ic3ia [13], an efficient open-source model checker for invariant and LTL properties, as well as its recent extensions ProphIC3 [14] (for discovering universally quantified invariants over arrays) and Lambda [7] (for the verification of parametric systems).…”

“…VMT-LIB is fully supported by the nuXmv [4] model checker, and it has been used as a benchmark format in several publications over the last few years (e.g. [6,14,11,7,5]).…”