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- W174998738 abstract "In this paper, we generalise the famous algorithm for swapping the contents of two variables without using a buffer. We introduce a novel combinatorial framework for procedural programming languages, where programs are only allowed to update one variable at a time. We first consider programs which do not have any additional memory. We prove that any function of all the variables can be computed this way in a number of updates which grows linearly with the number of variables. Similarly, any linear function can be computed using a linear number of linear instructions. We then derive the exact number of instructions required to compute any manipulation of variables. Second, we show that allowing programs to use additional memory is also incorporated in our framework. We quantify the gains obtained by using additional memory. This leads to shorter programs and allows to use only binary instructions, which is not sufficient in general when no memory is used." @default.
- W174998738 created "2016-06-24" @default.
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- W174998738 date "2011-11-25" @default.
- W174998738 modified "2023-09-27" @default.
- W174998738 title "Computing without memory" @default.
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