Decomposition of Boolean Functions – Recognizing a Good Solution by Traces

The problem of sequent two-block decomposition of a Boolean function is regarded in case when a good solution does exist. The problem consists mainly in finding an appropriate weak partition on the set of arguments of the considered Boolean function, which should be decomposable at that partition. A new fast heuristic combinatorial algorithm is offered for solving this task. At first the randomized search for traces of such a partition is fulfilled. The recognized traces are represented by some "triads" - the simplest weak partitions corresponding to non-trivial decompositions. After that the whole sought-for partition is restored from the discovered trace by building a track initialized by the trace and leading to the solution. The results of computer experiments testify the high practical efficiency of the algorithm.

Synthesis Methods of Multiple-valued Structures of Language Systems

The basic construction concepts of many-valued intellectual systems, which are adequate to primal problems of person activity and using hybrid tools with many-valued of coding are considered. The many-valued intellectual systems being two-place, but simulating neuron processes of space toting which are different on a level of actions, inertial and threshold of properties of neurons diaphragms, and also modification of frequency of following of the transmitted messages are created. All enumerated properties and functions in point of fact are essential not only are discrete on time, but also many-valued.

The Knowledge: Its Presentation and Role in Recognition Systems

The concept of knowledge is the central one used when solving the various problems of data mining and pattern recognition in finite spaces of Boolean or multi-valued attributes. A special form of knowledge representation, called implicative regularities, is proposed for applying in two powerful tools of modern logic: the inductive inference and the deductive inference. The first one is used for extracting the knowledge from the data. The second is applied when the knowledge is used for calculation of the goal attribute values. A set of efficient algorithms was developed for that, dealing with Boolean functions and finite predicates represented by logical vectors and matrices.

Implementation of a Heuristic Method of Decomposition of Partial Boolean Functions

An original heuristic algorithm of sequential two-block decomposition of partial Boolean functions is researched. The key combinatorial task is considered: finding of suitable partition on the set of arguments, i. e. such one, on which the function is separable. The search for suitable partition is essentially accelerated by preliminary detection of its traces. Within the framework of the experimental system the efficiency of the algorithm is evaluated, the boundaries of its practical application are determined.

Multiple-Valued Structures of Intellectual Systems

The basic construction concepts of many-valued intellectual systems, which are adequate to primal problems of person activity and using hybrid tools with many-valued intellectual systems being two-place, but simulating neuron processes of space toting which are different on a level of actions, inertial and threshold of properties of neuron diaphragms, and also frequency modification of the following transmitted messages are created. All enumerated properties and functions in point of fact are essential not only are discrete on time, but also many-valued.

Practical Stability and Vector-Lyapunov Functions for Impulsive Differential Equations with "Supremum"

Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

On the Residuum of Concave Univalent Functions

2000 Mathematics Subject Classification: 30C25, 30C45.