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Many CAD for VLSI techniques use time-frame expansion, also known as the iterative logic array representation, to model the sequential behavior of a system. Replicating industrial-size designs for many time-frames may impose impractically excessive memory requirements. This work proposes a performance-driven, succinct and parametrizable quantified Boolean formula (QBF) satisfiability encoding and its hardware implementation for modeling sequential circuit behavior. This encoding is then applied to three notable CAD problems, namely bounded model checking (BMC), sequential test generation and design debugging. Extensive experiments on industrial circuits confirm outstanding run-time and memory gains compared to state-of-the-art techniques, promoting the use of QBF in CAD for VLSI.