Abstract
An extension of a result by Grigoryev is used to derive a lower bound on the space-time product required for integer multiplication when realized by straight-line algorithms. If S is the number of temporary storage locations used by a straight-line algorithm on a random-access machine and T is the number of computation steps, then we show that (S+1)T ⩾ Ω(n2) for binary integer multiplication when the basis for the straight-line algorithm is a set of Boolean functions.
INDEX TERMS: space-time tradeoffs, pebble game, integer multiplication, straight-line algorithm.
This work was supported in part by the National Science Foundation under Grant MCS 76-20023.
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Savage, J.E., Swamy, S. (1979). Space-time tradeoffs for oblivious integer multiplication. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09510-1_40
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DOI: https://doi.org/10.1007/3-540-09510-1_40
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