Is the data encryption standard a group?
Proc. of a workshop on the theory and application of cryptographic techniques on Advances in cryptology---EUROCRYPT '85
Notes on recursion elimination
Communications of the ACM
Efficient reducibility between programming systems (Preliminary Report)
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Degrees of translatability and canonical forms in program schemas: Part I
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
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We consider the class of linear recursive programs. A linear recursive program is a set of procedures where each procedure can make at most one recursive call. The conventional stack implementation of recursion requires time and space both proportional to n, the depth of recursion. It is shown that in order to implement linear recursion so as to execute in time n one doesn''t need space proportional to n: $n^\epsilon$ for arbitrarily small $\epsilon$ will do. It is also known that with constant space one can implement linear recursion in time $n^2$. We show that one can do much better: $n^{1+\epsilon}$ for arbitrarily small $\epsilon$. We also describe an algorithm that lies between these two: it takes time n.log(n) and space log(n). It is shown that several problems are closely related to the linear recursion problem, for example, the problem of reversing an input tape given a finite automaton with several one-way heads. By casting all these problems into a canonical form, efficient solutions are obtained simultaneously for all.