Showing papers in "Acta Cybernetica in 1973"

Generalized context-free grammars.

Abstract: 1 . Introduction. Generalized context-free grammars can be thought of as contextfree grammars all rules of which are of the form A where a is a regular expression. Generalized context-free grammars and their representation by a set of finitestate diagrams are a convenient tool to describe context-free languages. In this paper a classification of context-free languages according to the minimal number of non-terminals of generalized context-free grammars is studied and the corresponding decision problems are investigated.

Combined application of drawing and steepest descent in generating initial estimates for subsequent optimization.

Abstract: The determination of the unrestricted local minimum of a function of several variables by the \"direct search\" methods consists in the sequential examination of function values belonging to randomly selected vectors as the independent variables. A comparison of each trial solution with the \"best\" one up to that time helps locate the approximate value of the minimum. Even the more sophisticated gradient methods [1, 2, 3] cannot dispense with a similar method for generating initial estimates for subsequent iterative optimization. In certain cases (e.g. in the Gauss—-Newton method) a favourably chosen initial value is a prerequisite of convergence, whereas in others it allows the gradient method to be used for finding the absolute minimum of a function in a bounded region. Finally, the number of iterations can be reduced considerably if a good initial estimate of the minimum is available. We have found that the effectiveness of this method can be substantially improved if the initial estimate is chosen not as the vector corresponding to the lowest function value but, starting with the drawn vector, a step is performed according to the principles of the steepest descent and the function values are compared in these modified points. Both methods are described f rom the viewpoint of probability, and some problems of application encountered in practice are discussed.

The notion and some applications of generalized initial segment.

Abstract: In computational practice we are often confronted with situations where we have to handle strings composed of elements that can be put into two disjoint classes according to the way they influence the outcome of the operations to be performed on these strings. E.g. this happens in the case of translating higher-level programming languages. A programme written in such a language is a combination of terminators (operation symbols, parentheses, etc.) and quantities (identifiers and numbers, these are composed of letters and numerals). During translation the terminators control the compiler, while quantities play only a passive role: the translation process is not influenced e.g! by replacing each occurrence of an identifier with occurrences of another, while a similar statement for terminators is obviously false. Other types of formula-handling algorithms serve also as good examples in which such mixedsequence situations arise. In the present article we are going to define the notion of generalized initial segment for strings composed of elements of two disjoint sets. This notion simultaneously extends those of initial segment and of subsequence. We also present an algorithm which can decide whether or not any string is a generalized initial segment of another. The applicability in practice of the algorithm is illustrated with two examples. The second one of these deals with the Universal Decimal Classification (UDC), which is generally used in library practice. The ideas outlined in this context have been used in an information-retrieval system here working on the basis of UDC.