Kraft storage and access for list implementations(Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
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Consider a machine with a cellular memory used to store a list X , where X is a finite alphabet and i N. We investigate the machine representation of such a list and the implementation of common list operations such as determining the i element and adding to deleting an element. Information-theoretic arguments are used in order to obtain lower bounds on storage and access costs for implementing variable-length lists and, in particular, stacks. Representations are discussed which attain these bounds separately and can sometimes attain both, although it is shown that some common representations of stacks cannot simultaneously achieve both. On the constructive side, we show that it is possible to implement a stack of any finite length so as to achieve Kraft storage and so that the number of memory cell accesses required to perform a PUSH or a TOP operation is always O(log n) but where, assuming a non-increasing probability distribution on stack lengths, a POP operation requires on the average only a constant number of accesses.