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

Bandwidth and Wavefront Reduction for Static Variable Ordering in Symbolic Reachability Analysis

We investigate the use of bandwidth and wavefront reduction algorithms to determine a static BDD variable ordering. The aim is to reduce the size of BDDs arising in symbolic reachability. Previous work showed that minimizing the (weighted) event span of the variable dependency graph yields small BDDs. The bandwidth and wavefront of symmetric matrices are well studied metrics, used in sparse matrix solvers, and many bandwidth and wavefront reduction algorithms are readily available in libraries like Boost and ViennaCL.\ud In this paper, we transform the dependency matrix to a symmetric matrix and apply various bandwidth and wavefront reduction algorithms, measuring their influence on the (weighted) event span. We show that Sloan’s algorithm, executed on the total graph of the dependency matrix, yields a variable order with minimal event span. We demonstrate this on a large benchmark of Petri nets, Dve, Promela, B, and mcrl2 models. As a result, good static variable orders can now be determined in milliseconds by using standard sparse matrix solvers