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

Witness generation in existential CTL model checking

Hardware and software systems are widely used in applications where failure is prohibitively costly or even unacceptable. The main obstacle to make such systems more reliable and capable of more complex and sensitive tasks is our limited ability to design and implement them with sufficiently high degree of confidence in their correctness under all circumstances. As an automated technique that verifies the system early in the design phase, model checking explores the state space of the system exhaustively and rigorously to determine if the system satisfies the specifications and detect fatal errors that may be missed by simulation and testing. One essential advantage of model checking is the capability to generate witnesses and counterexamples. They are simple and straightforward forms to prove an existential specification or falsify a universal specification. Beside enhancing the credibility of the model checker\u27s conclusion, they either strengthen engineers\u27 confidence in the system or provide hints to reveal potential defects. In this dissertation, we focus on symbolic model checking with specifications expressed in computation tree logic (CTL), which describes branching-time behaviors of the system, and investigate the witness generation techniques for the existential fragment of CTL, i.e., ECTL, covering both decision-diagram-based and SAT-based. Since witnesses provide important debugging information and may be inspected by engineers, smaller ones are always preferable to ease their interpretation and understanding. To the best of our knowledge, no existing witness generation technique guarantees the minimality for a general ECTL formula with nested existential CTL operators. One contribution of this dissertation is to fill this gap with the minimality guarantee. With the help of the saturation algorithm, our approach computes the minimum witness size for the given ECTL formula in every state, stored as an additive edge-valued multiway decision diagrams (EV+MDD), a variant of the well-known binary decision diagram (BDD), and then builds a minimum witness. Though computationally intensive, this has promising applications in reducing engineers\u27 workload. SAT-based model checking, in particular, bounded model checking, reduces a model checking problem problem into a satisfiability problem and leverages a SAT solver to solve it. Another contribution of this dissertation is to improve the translation of bounded semantics of ECTL into propositional formulas. By realizing the possibility of path reuse, i.e., a state may build its own witness by reusing its successor\u27s, we may generate a significantly smaller formula, which is often easier for a SAT solver to answer, and thus boost the performance of bounded model checking

New metrics for static variable ordering in decision diagrams

Abstract. We investigate a new class of metrics to find good variable orders for decision diagrams in symbolic state-space generation. Most of the previous work on static ordering is centered around the concept of minimum variable span, which can also be found in the literature under several other names. We use a similar concept, but applied to event span, and generalize it to a family of metrics parameterized by a moment, where the metric of moment 0 is the combined event span. Finding a good variable order is then reduced to optimizing one of these metrics, and we design extensive experiments to evaluate them. First, we investigate how the actual optimal order performs in state-space generation, when it can be computed by evaluating all possible permutations. Then, we study the performance of these metrics on selected models and compare their impact on two different state-space generation algorithms: classic breadth-first and our own saturation strategy. We conclude that the new metric of moment 1 is the best choice. In particular, the saturation algorithm seems to benefit the most from using it, as it achieves the better performance in nearly 80 % of the cases.