In this paper, we develop a new technique called buffer merging for reducing memory requirements of synchronous dataflow (SDF) specifications. SDF has proven to be an attractive model for specifying DSP systems, and is used in many commercial tools like DSPCanvas, SPW, and COSSAP. Good synthesis from an SDF specification depends crucially on scheduling, and memory is an important metric for generating efficient schedules. Previous techniques on memory minimization have either not considered buffer sharing at all, or have done so at a fairly coarse level (the meaning of this will be made more precise in the paper). In this paper, we develop a buffer overlaying strategy that works at the level of an input/output edge pair of an actor. It works by algebraically encapsulating the lifetimes of the tokens on the input/output edge pair, and determines the maximum amount of the input buffer space that can be reused by the output. We develop the mathematical basis for performing merging operations, and develop several algorithms and heuristics for using the merging technique for generating efficient implementations. We show improvements of up to 54% over previous techniques. (Also cross-referenced as UMIACS-TR-2000-20)