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On compiling algorithms for arithmetic expressions
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The majority of computers that have been built have performed all computations in devices called accumulators, or registers. In this paper, it is shown that the problem of generating minimal-length code for such machines is hard in a precise sense; specifically it is shown that the problem is NP-complete. The result is true even when the programs being translated are arithmetic expressions. Admittedly, the expressions in question can become complicated.