Component-wise incremental LTL model checking

Efficient symbolic and explicit-state model checking approaches have been developed for the verification of linear time temporal logic (LTL) properties. Several attempts have been made to combine the advantages of the various algorithms. Model checking LTL properties usually poses two challenges: one must compute the synchronous product of the state space and the automaton model of the desired property, then look for counterexamples that is reduced to finding strongly connected components (SCCs) in the state space of the product. In case of concurrent systems, where the phenomenon of state space explosion often prevents the successful verification, the so-called saturation algorithm has proved its efficiency in state space exploration. This paper proposes a new approach that leverages the saturation algorithm both as an iteration strategy constructing the product directly, as well as in a new fixed-point computation algorithm to find strongly connected components on-the-fly by incrementally processing the components of the model. Complementing the search for SCCs, explicit techniques and component-wise abstractions are used to prove the absence of counterexamples. The resulting on-the-fly, incremental LTL model checking algorithm proved to scale well with the size of models, as the evaluation on models of the Model Checking Contest suggests

Constraint Programming with Multi-valued Decision Diagrams: A Saturation Approach

Constraint programming is a declarative way of modeling and solving optimization and satisfiability problems over finite domains. Traditional solvers use search-based strategies enhanced with various optimizations to reduce the search space. One of such techniques involves multi-valued decision diagrams (MDD) to maintain a superset of potential solutions, gradually discarding combinations of values that fail to satisfy some constraint. Instead of the relaxed MDDs representing a superset, we propose to use exact MDDs to compute the set of solutions directly without search, compactly encoding all the solutions instead of enumerating them. Our solution relies on the main idea of the saturation algorithm used in model checking to reduce the required computational cost. Preliminary results show that this strategy can keep the size of intermediate MDDs small during the computation