In this article, we revisit the topic of generalizing proof obligations (POs) in bit-level property directed reachability (PDR). We provide a comprehensive study which: 1) determines the complexity of the problem; 2) thoroughly analyzes limitations of existing methods; 3) introduces approaches to PO generalization that have never been used in the context of PDR; 4) compares the strengths of different methods from a theoretical point of view; and 5) intensively evaluates the methods on various benchmarks from the hardware model checking as well as from AI planning.

If embedded systems are used in safety-critical environments, they need to meet several standards. For example, in the automotive domain the ISO 26262 standard requires that the software running on such systems does not contain unreachable code. Software model checking is one effective approach to automatically detect such dead code. Being used in a commercial product, iSAT3 already performs very well in this context. In this paper we integrate IC3 into iSAT3 in order to improve its dead code detection capabilities even further.

We describe a thoroughly interweaved forward and backward version of PDR/IC3 called fbPDR. Motivated by the complementary strengths of PDR and Reverse PDR and by related work showing the benefits of collaboration between the two, fbPDR lifts the combination to a new level. We lay the theoretical foundations for sharing information represented by learned lemmas between PDR and Reverse PDR and demonstrate the effectiveness of our approach on benchmarks from the Hardware Model Checking Competition.

In the last few years IC3 resp. PDR attracted a lot of attention as a SAT-based hardware verification approach without needing to unroll the transition relation as in Bounded Model Checking (BMC). Motivated by different strengths of forward and backward traversal already observed in BDD based model checking and by an exponential complexity gap between original PDR and its reverted counterpart `Reverse PDR' (which starts its analysis with the initial states instead of the unsafe states as in the original PDR), we take a closer look at Reverse PDR and we present a combined forward/backward version of PDR that inherits the advantages of both original and Reverse PDR. Our experimental results on benchmarks from the Hardware Model Checking Competition demonstrate clear benefits of the combined approach.