Abstract. We show that classic PRE is also a maximum flow problem, thereby revealing the missing link between classic and speculative PRE, and more importantly, establishing a common high-level conceptual basis for this important compiler optimisation. To demonstrate this, we formulate a new, simple unidirectional bit-vector algorithm for classic PRE based only on the well-known concepts of availability and anticipatability. Designed to find a unique minimum cut in a flow network derived from a CFG, which is proved simply but rigorously, our algorithm is simple and intuitive, and its optimality is self-evident. This conceptual simplicity also translates into efficiency, as validated by experiments.