Space-time tradeoffs for linear recursion

AbstractA 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.