M. Ishihara,∗ M. Tanaka,∗∗ and K. Kuriyama∗∗


Cubic systolic arrays, systolic arrays, filling problems, informatic- cube worlds, tiling


This paper introduces a cubic systolic array and discusses its properties to remark another dimension of a systolic array. A cubic systolic array is a three-dimensional systolic array and features PEs arranged in various directions in a three-dimensional lattice space. Those PEs are communicated with the six adjacent PEs and they are synchronized by global clocks. In a cubic systolic array, a port of a PE is connected to a specified port of an adjacent PE. This is called one-to-one correspondence between ports. One-to-one correspondence is a necessary condition for systolic arrays. Typical systolic arrays hold this condition implicitly by arranging their PEs in the same direction. A cubic systolic array, meanwhile, allows PEs to be arranged in various directions by holding one-to-one correspondence directly. This paper shows that all kinds of one- to-one correspondence between ports are available to cubic systolic arrays so that their PEs are arranged in various directions and then it illustrates five kinds of cubic systolic arrays characterizing cellular automata, shared memories, typical systolic arrays, neural networks, and pipeline memories.

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