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This paper presents a new approach to the analysis of performance of the various key-to-address transformation methods. In this approach the keys in a file arc assumed to have been selected from the key space according to a certain probabilistic selection algorithm. All files with the same number of keys selected from this key space will be suitably weighted in accordance with the algorithm, and the average performance of the transformation methods on these files will be used as the potential of these methods. Using this analysis, methods with the same overall performance can be classified and key distributions partial to certain transformations can be identified. All this can be done analytically. The approach is applied to a group of transformation methods using files whose keys are selected randomly. [ABSTRACT FROM AUTHOR]

Given the horizontal and vertical projections of a finite binary pattern f, can we reconstruct the original pattern f? In this paper we give a characterization of patterns that ore reconstructable from their projections. Three algorithms ore developed to reconstruct both unambiguous and ambiguous patterns, it is shown that an unambiguous pattern can be perfectly reconstructed in time m × n and that a pattern similar to an ambiguous pattern can also be constructed in time m × n, where m, n are the dimensions of the pattern frame. [ABSTRACT FROM AUTHOR]

This paper presents a canonical form for context-sensitive derivations and a parsing algorithm which finds each context-sensitive analysis once and only once. The amount of memory required by the algorithm is essentially no more than that required to store a single complete derivation. In addition, a modified version of the basic algorithm is presented which blocks infinite analyses for grammars which contain loops. The algorithm is also compared with several previous parsers for context-sensitive grammars and general rewriting systems, and the difference between the two types of analyses is discussed. The algorithm appears to be complementary to an algorithm by S. Kuno in several respects, including the space-time trade-off and the degree of context dependence involved. [ABSTRACT FROM AUTHOR]

The article discusses the computation of rational approximations using existing algorithms. In a recent paper it is shown that minimax logarithmic approximations are optimal for square root calculations, making the minimax logarithmic problem of practical interest. The authors point out how rational approximations which are best with respect to maximum logarithmic error can be computed by existing algorithms. Suppose one wishes to approximate a positive continuous function "f" by a positive rational function R, then the logarithmic error at a point x is log (f(x))-- log (R(x)). The approximation problem is thus equivalent to ordinary approximation of continuous function g = log (f) by log {R).

Neely has discussed computational error generated by some algorithms used to compute various statistics. In the present paper methods are described which are error-free, simple in concept, and usually less costly in machine time than those mentioned by Neely. [ABSTRACT FROM AUTHOR]