Recent research has investigated time-space tradeoffs for register allocation strategies of certain fixed sets of expressions. This paper is concerned with the time-space tradeoff for register allocation strategies of any set of expressions which compute given functions. Time-space tradeoffs for pebbling superconcentrators and grates are developed. Corollaries which follow include tradeoffs for any straight-line program which computes polynomial multiplication, polynomial convolution, the discrete Fourier transform, oblivious merging, and most sets of linear forms.
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Martin Tompa (1978) studied this question.