Abstract
A linear recursive procedure is one each of whose executions activates at most one invocation of itself. When linear recursion cannot be replaced by iteration, it is usually implemented with a stack of size proportional to the depth of recursion. In this paper we analyze implementations of linear recursion which permit large reductions in storage space at the expense of a small increase in computation time. For example, if the depth of recursion isn, storage space can be reduced to\(\sqrt n \) at the cost of a constant factor increase in running time. The problem is treated by abstracting any implementation of linear recursion as the pebbling of a simple graph, and for this abstraction we exhibit the optimal space-time tradeoffs.
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This work was supported in part by the National Science Foundation under Grant MCS 76-20023, and in part by the Joint Services Electronics Program (U.S. Army, U.S. Navy, and U.S. Air Force) under Contract N00014-79-C-0424.
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Swamy, S., Savage, J.E. Space-time tradeoffs for linear recursion. Math. Systems Theory 16, 9–27 (1983). https://doi.org/10.1007/BF01744566
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DOI: https://doi.org/10.1007/BF01744566