Showing papers on "Time complexity published in 1968"

An efficient context-free parsing algorithm

Abstract: A parsing algorithm which seems to be the most efficient general context-free algorithm known is described. It is similar to both Knuth's LR(k) algorithm and the familiar top-down algorithm. It has a time bound proportional to n3 (where n is the length of the string being parsed) in general; it has an n2 bound for unambiguous grammars; and it runs in linear time on a large class of grammars, which seems to include most practical context-free programming language grammars. In an empirical comparison it appears to be superior to the top-down and bottom-up algorithms studied by Griffiths and Petrick.

Accelerated method of solving the linear time optimal problem

Abstract: AT the present time there are a number of methods enabling the linear time-optimal problem to be solved [1–4]. These methods, fairly similar to one another in idea, possess common drawbacks: they are generally iteration methods with slow convergence. Hence it is extremely important in practive to construct rapidly convergent iteration processes for solving this problem. This problem was formulated in [5] where one such method, that of L. W. Neustadt, was analyzed. In particular, it was shown that it possesses convergence of the first order with a convergence factor close to unity. We notice that this analysis may be transferred to other methods of this type also. Moreover, in [5] a method of second-order convergence was constructed. However, this method is very unwieldy and not well adapted for realization on a computer. In this paper a fairly simple iteration method of solving time optimal problems is constructed which possesses an accelerated rate of convergence. This method is constructed by combining the methods of [3] and [6].