Accelerate Safety Model Checking Based on Complementary Approximate Reachability

Model checking is an automatic formal verification method that is widely applied to hardware verification. Safety properties are the mainly verified properties in practice that can be falsified within finite steps if they do not hold for systems. However, state-of-the-art safety model-checking algorithms cannot meet the performance requirement driven by the industry as the sizes of (hardware) systems to be verified increase rapidly. Therefore, more efficient techniques are still eagerly in demand. Recently, a new safety model-checking technique complementary approximate reachability (CAR) was presented and received considerable concerns from the community. CAR has shown its advantages in unsafe checking (bug finding), but cannot be as competitive as other state-of-the-art techniques, e.g., IC3/PDR, on safe checking (proving correctness). In this article, we propose four kinds of heuristics, two inspired by IC3/PDR and another two dedicated to CAR, to improve the performance of CAR. We integrate the heuristics into the open-source model checker SimpleCAR and compare the performance to the original CAR and IC3/PDR on 748 instances from the hardware model-checking competitions. Our results show that by fixing the time and memory resources, CAR can solve 124 more instances with the four proposed heuristics, i.e., 53.4% more instances can be solved comparing to the original CAR. Furthermore, CAR in both forward and backward directions can solve ten more instances than IC3/PDR in corresponding directions, and uniquely solve 44 more instances that IC3/PDR in corresponding directions cannot solve, which increases the capability of the current model-checking portfolio.