Many performance-critical applications perform bitwise computations over bitstreams for better performance or higher space efficiency, such as multimedia processing and bitmap indexing. However, when these bitwise computations carry dependences, the entire bitstream traversal becomes serial, fundamentally limiting the scalability. In this work, we show that bitstream-carried dependences are actually “breakable” in many cases, with the adoption of a systematic treatment, called principled bitwise speculation (PBS). The core idea of PBS stems from an analogy drawn between bitstream programs and sequential circuits, both of which transform binary sequences. From this new perspective, it becomes natural to model the dependences in bitstream programs with finite-state machines (FSM), a basic model for sequential circuits. To achieve this, PBS features an assembly of static analyses that reason about bitstream programs down to the bit level to identify the bits causing dependences, then it treats the value combinations of dependent bits as states to construct FSMs. The modeling, for the first time, enables the use of FSM speculation techniques to parallelize bitstream programs. Basically, by leveraging the state convergence of FSMs, the values of dependent bits can be predicted with much higher accuracies. In cases the predication fails, PBS tries to directly “rectify” the wrong outputs based on bitwise logic, minimizing the mis-speculation costs. Besides prediction, FSM shows higher execution efficiency than the original program in some cases, making itself an optimized version to accelerate serial bitstream processing. We prototyped PBS using LLVM. Evaluation with real-world bitstream programs confirms the effectiveness of PBS, showing up to near-linear speedup on multicore machines. In particular, PBS significantly boosts the scalability of a state-of-the-art regular expression engine.