This paper describes the NUXMV symbolic model checker for finiteand infinite-state synchronous transition systems. NUXMV is the evolution of the NUSMV open source model checker. It builds on and extends NUSMV along two main directions. For finite-state systems it complements the basic verification techniques of NUSMV with state-of-the-art verification algorithms. For infinitestate systems, it extends the NUSMV language with new data types, namely Integers and Reals, and it provides advanced SMT-based model checking techniques.Besides extended functionalities, NUXMV has been optimized in terms of performance to be competitive with the state of the art. NUXMV has been used in several industrial projects as verification back-end, and it is the basis for several extensions to cope with requirements analysis, contract based design, model checking of hybrid systems, safety assessment, and software model checking.This work was carried out within the D-MILS project, which is partially funded under the European Commission's Seventh Framework Programme (FP7).

We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with Implicit (predicate) Abstraction, a technique that expresses abstract transitions without computing explicitly the abstract system and is incremental with respect to the addition of predicates. In this scenario, IC3 operates only at the Boolean level of the abstract state space, discovering inductive clauses over the abstraction predicates. Theory reasoning is confined within the underlying SMT solver, and applied transparently when performing satisfiability checks. When the current abstraction allows for a spurious counterexample, it is refined by discovering and adding a sufficient set of new predicates. Importantly, this can be done in a completely incremental manner, without discarding the clauses found in the previous search. The proposed approach has two key advantages. First, unlike current SMT generalizations of IC3, it allows to handle a wide range of background theories without relying on ad-hoc extensions, such as quantifier elimination or theory-specific clause generalization procedures, which might not always be available, and can moreover be inefficient. Second, compared to a direct exploration of the concrete transition system, the use of abstraction gives a significant performance improvement, as our experiments demonstrate.

HYCOMP is a model checker for hybrid systems based on Satisfiability Modulo Theories (SMT). HYCOMP takes as input networks of hybrid automata specified using the HyDI symbolic language. HYCOMP relies on the encoding of the network into an infinite-state transition system, which can be analyzed using SMT-based verification techniques (e.g. BMC, K-induction, IC3). The tool features specialized encodings of the automata network and can discretize various kinds of dynamics.HYCOMP can verify invariant and LTL properties, and scenario specifications; it can also perform synthesis of parameters ensuring the satisfaction of a given (invariant) property. All these features are provided either through specialized algorithms, as in the case of scenario or LTL verification, or applying off-theshelf algorithms based on SMT. We describe the tool in terms of functionalities, architecture, and implementation, and we present the results of an experimental evaluation.This work was carried out within the D-MILS project, which is partially funded under the European Commission's Seventh Framework Programme (FP7).

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