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This paper presents a novel approach to the synthesis of interleaved memory systems that is especially suited for application-specific processors. Our synthesis system generates the optimized interleaved memories for a specific algorithm and finds the best mapping of arrays in that algorithm onto the memory system to achieve high performance. The design space is four-dimensional (4-D) and comprises the number of memory banks, the type of memory components, the storage scheme, and the range of clock period in the system. Optimal designs are found among the Pareto points (a set of nondominated points in the design space) computed for our memory model under the performance and cost criteria set by the designer. The memory model includes all the components of an interleaved memory system and covers a lookup table-based address generation with data alignment. The synthesis is based on a general periodic storage scheme, which enables efficient handling of irregular and overlapped access patterns. The synthesis process is the exhaustive search of the heavily pruned design space, and the pruning is based on mathematically proven properties of periodic storage schemes. This paper presents the theorems, the synthesis algorithm, and the methods of effective word and bank address generation. Examples are given to illustrate the effectiveness of our method.