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A new algorithm for testing primality is presented. The algorithm is distinguishable from the lovely algorithms of Solvay and Strassen [36], Miller [27] and Rabin [32] in that its assertions of primality are certain (i.e., provable from Peano's axioms) rather than dependent on unproven hypothesis (Miller) or probability (Solovay-Strassen, Rabin). An argument is presented which suggests that the algorithm...
Several representations of P, the class of deterministic polynomial time acceptable languages, are compared with respect to succinctness. It is shown that requirements such as polynomial running time, verifiability of running time, and verifiability of accepting a set in P can be causes for differences in succinctness that are not recursively bounded. Relating succinctness to nondeterminism, it is...
The acceleration of matrix multiplication MM, is based on the combination of the method of algebraic field extension due to D. Bini, M. Capovani, G. Lotti, F. Romani and S. Winograd and of trilinear aggregating, uniting and canceling due to the author. A fast algorithm of O(N2.7378) complexity for N × N matrix multiplication is derived. With A. Schönhage's Theorem about partial and total MM, our approach...
Traditional implementations of conditional critical regions and monitors can lead to unproductive "busy waiting" if processes are allowed to wait on arbitrary boolean expressions. Techniques from global flow analysis may be employed at compile time to obtain information about which critical regions (monitor calls) are enabled by the execution of a given critical region (monitor call). We...
Fully polynomial approximation algorithms for knapsack problems are presented. These algorithms are based on ideas of Ibarra and Kim, with modifications which yield better time and space bounds, and also tend to improve the practicality of the procedures. Among the principal improvements are the introduction of a more efficient method of scaling and the use of a median-finding routine to eliminate...
A combinatorial problem related to storage allocation is analyzed. The problem falls into a class of NP-complete, one-dimensional bin-packing problems. We propose an iterative approximation algorithm and show that it is superior to an earlier heuristic presented for this problem. The bulk of the paper is devoted to the proof of a worst-case performance bound.
Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O(√n) vertices. This separator theorem, in combination with a divide-and-conquer strategy, leads to many new complexity results for planar graph problems. This paper describes some of these results.
We employ elementary results from the theory of several complex variables to obtain a quadratic lower bound on the complexity of computing the mean distance between points in the plane. This problem has 2N inputs and a single output and we show that exactly N(N-1)/2 square roots must be computed by any program over +, -, ×, ÷,) √, log and comparisons, even allowing an arbitrary field of constants...
Decision procedures for validity in intuitionistic propositional calculus and modal propositional calculus are given which require a running time proportional to a polynomial in the length of the formula on a nondeterministic Turing machine. Using a theorem of Cook's and well-known transformations from intuitionistic to classical and modal to intuitionistic logics, the validity problem for intuitionistic...
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