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Two decidable logical theories are presented, one complete for deterministic polynomial time, one complete for polynomial space. Both have natural proof systems. A lower space bound of n/log(n) is shown for the proof system for the PTIME complete theory and a lower length bound of 2cn/log(n) is shown for the proof system for the PSPACE complete theory.
A model for searching algorithms is developed which includes most tree-like searching structures such as lists, binary trees, AVL trees and 2, 3-trees. It is shown that no searching algorithm employing a data structure that is uniquely represented (up to isomorphism) can provide search, insert and delete functions all operating faster than c√n time for every n key tree. The c√n bound is shown to be...
We define alternating Turing Machines which are like nondeterministic Turing Machines, except that existential and universal quantifiers alternate. Alternation links up time and space complexities rather well, in that alternating polynomial time equals deterministic polynomial space, and alternating linear space equals deterministic exponential time. Such considerations lead to a two-person game complete...
Motivated by an elementary programming system for formal language generation, we propose a generalized a pushdown acceptor which uses both a checking stack and a pushdown store in original manner. In the analysis of the machine-model parallel rewriting appears to be a fundamental tool for breaking the implicit recursion-structure. Variations of the machine-model (in the sense of Cook) lead to a natural...
Given a particular computer system the extension problem concerns the prediction of performance when the size of main memory is increased. In this paper a specific approach to this problem is formulated for demand paging systems. A necessary and sufficient condition on the nature of page replacement rules which leads to solutions of the extension problem is a major result of the paper. As the other...
An n-dimensional iterative array of finitestate machines (abbreviated nD) is a special type of real-time tape acceptor. The principal results are as follows: 1. nD's have equivalent forms With simplified stencils and length k encodings of the input alphabet. 2. The set of palindromes and the set of tapes of the form ττ are accepted by 1D's. 3. The sets of tapes accepted by nD's are a Boolean algebra...
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