Simple Minimization Method of the Variables Number in Complete and Incomplete Logic Functions. Part 1

A new minimization method of the variables number in complete and incomplete logic functions, based on the procedure of conjuncterms splitting is proposed. The advantages of the proposed method are illustrated by examples of determining nonessential variables in the functions, which are borrowed from the well-known publications.Предложен новый метод минимизации числа переменных в полных и неполных логических функциях, основанный на процедуре расцепления конъюнктермов. Преимущества предложенного метода иллюстрируют примеры определения несущественных переменных в функциях, заимствованных автором из известных публикаций с целью сравнения.Запропоновано новий метод мінімізації кількості змінних у повних і неповних логічних функціях, що ґрунтується на процедурі розчеплення кон'юнктермів. Переваги пропонованого методу ілюструють приклади визначення неістотних змінних у функціях, які автор запозичив з відомих публікацій з метою порівняння

Multiple-Valued Index Generation Functions: Reduction of Variables by Linear Transformation

We consider incompletely specified multiple-valued input index generation functions f : D → {1, 2, . . . , k}, where D ⊆ P n and P = {0, 1, 2, . . . , p − 1}. In such functions, the number of variables to represent f can be often reduced. Let k be the number of elements in D. We show that most functions can be represented with 2 log p (k + 1) or fewer variables, when k is sufficiently smaller than p n . Also, to further reduce the number of variables, we use linear transformations. To find good linear transformations, we introduce the imbalance measure and the ambiguity measure. A heuristic algorithm to reduce the number of variables by linear transformation is presented. Experimental results using randomly generated functions and lists of English words are shown

Generalized contexts for reaction systems: definition and study of dynamic causalities

Reaction systems are a qualitative formalism for the modelling of systems of biochemical reactions. In their original formulation, a reaction system executes in an environment (or context) that can supply it with new objects at each evolution step. The context drives the behaviour of a reaction system: it can provide different inputs to the system that can lead to different behaviours. In order to more faithfully deal with open systems, in this paper we propose a more powerful notion of context having not only the capability to provide objects, but also to absorb (or remove) objects at each evolution step. For such reaction systems with generalized context we investigate properties of dynamic causality by revising the previously proposed concept of formula based predictor. A formula based predictor is a Boolean formula characterising all contexts that lead to the production of a certain object after a given number of steps. In this paper, we revise the theory of formula based predictors in order to deal with reaction systems executed in a context of the new kind. As applications, we show an example of interaction between biochemical pathways and a reaction system modelling cell metabolism and respiration

The 1982 NASA/ASEE Summer Faculty Fellowship Program

A NASA/ASEE Summer Faculty Fellowship Research Program was conducted to further the professional knowledge of qualified engineering and science faculty members, to stimulate an exchange of ideas between participants and NASA, to enrich and refresh the research and teaching activities of participants' institutions, and to contribute to the research objectives of the NASA Centers