This thesis explores the time optimal implementation of computational graphs on a finite register machine. The implementation fully exploits the machine architecture, especially, the number of registers. The derived algorithms allow one to obtain time efficient implementations of a given graph in machines with a known number of registers. These optimization procedures are applied to digital signal processing graphs. It is shown that the regular structure of these graphs allows one to identify

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... mputational kernels which, when used repeatedly, can cover the entire graph. The l- and r-register implementations of Hadamard and Fast Fourier Transforms using various computational kernels are studied for their code sizes and time complexities. The results obtained also allow one to select an optimal hardware devoted to a particular computational application