Denis V. Popel

Information theoretic approach to minimization of polynomial expressions over GF(4)

This paper addresses a new information theoretic approach to minimization of polynomial expressions for Multiple Valued Logic (MVL) functions. Its focus is to determine the so-called pseudo Reed-Muller and pseudo Kronecker expressions of MVL functions. A key point of our approach is the use of information theoretic measures for efficient design of Decision Trees (DTs) to represent MVL functions. We utilize free pseudo Reed-Muller GF(4) (PSDRMGF) DTs and free pseudo Kronecker GF(4) (PSDKGF) DTs. Furthermore, we show that the suggested approach allows to manage the process of minimization in a simple way, for the most of known forms of logic function representation. Our program, Info-MV, produces, in most cases, the extremely better results, in contrast to some known heuristic minimization strategies.

Compact Graph Model of Handwritten Images: Integration into Authentification and Recognition

A novel algorithm for creating a mathematical model of curved shapes is introduced. The core of the algorithm is based on building a graph representation of the contoured image, which occupies less storage space than produced by raster compression techniques. Different advanced applications of the mathematical model are discussed: recognition of handwritten characters and verification of handwritten text and signatures for authentification purposes. Reducing the storage requirements due to the efficient mathematical model results in faster retrieval and processingt imes. The experimental outcomes in compression of contoured images and recognition of handwritten numerals are given.

From continuous to Multiple-valued data

In modern science, significant advances are typically made at cross-roads of disciplines. Thus, many optimization problems in Multiple-valued Logic Design have been successfully approached using ideas and techniques from Artificial Intelligence. In particular, improvements in multiple-valued logic design have been made by utilizing information/uncertainty measures. In this respect, the paper addresses the problem known as discretization and introduces a method of finding an optimal representation of continuous data in the multiple-valued domain. The paper introduces new information density measures and an optimization criterion. We propose an algorithm that incorporates new measures and is applied to both unsupervised and supervised discretization. The experimental results on continuous-valued benchmarks are given to demonstrate the efficiency and robustness of the algorithm.

Sierpinski gaskets for logic functions representation

This paper introduces a new approach to represent logic functions in the form of Sierpinski gaskets. The structure of the gasket allows it to be manipulated with the corresponding logic expression using the recursive essence of fractals. Thus, the Sierpinski gaskets pattern has myriad useful properties which can enhance the practical features of other graphic representations like decision diagrams. We have covered possible applications of Sierpinski gaskets in logic design and justified our assumptions in logic function minimization (both Boolean and multiple-valued cases). Experimental results on benchmarks with advances in the novel structure are considered as well.

Conquering Uncertainty in Multiple-Valued Logic Design

In modern science, significant advances are typically made atcross-roads of disciplines. Thus, many optimization problems inMultiple-valued Logic Design have been successfullyapproached using ideas and techniques from ArtificialIntelligence. In particular, improvements in multiple-valuedlogic design have been made by exploiting information/uncertaintymeasures. In this paper, we review well-known information measuresin the multiple-valued domain and consider some methods of findinginformation measures for completely or incompletely specifiedfunctions with multiple-valued and continuous attributes. In thisrespect, the paper addresses the problem known as discretizationand introduces a method of finding an optimal representation ofcontinuous data in the multiple-valued domain. We also propose atechnique for efficient calculation of different informationmeasures using Multiple-valued Decision Diagrams. As oneapplication of our technique, we outline an approach tosynthesizing digital circuits derived from decision diagrams thatcan yield to reduction in power dissipation. The paper also showsthe impact in several important areas of multiple-valued systemdesign including (i) fuzzy logic, (ii) quantum computing systems,and (iii) data mining.

On the information engine of circuit design

This paper addresses a new approach to find a spectrum of information measures for the process of digital circuit synthesis. We consider the problem from the information engine point of view. The circuit synthesis as a whole and different steps of the design process (an example of decision diagram is given) are presented via such measurements as entropy, logical work and information vitality. We also introduce new information measures to provide better estimates of synthesis criteria. We show that the basic properties of an information engine, such as the conservation law of information flow and the equilibrium law of information can be formulated.

Information measures in detecting and recognizing symmetries

This paper presents a method to detect and recognize symmetries in Boolean functions. The idea is to use information theoretic measures of Boolean functions to detect sub-space of possible symmetric variables. Coupled with the new techniques of efficient estimations of information measures on Binary Decision Diagrams (BDDs) we obtain promised results in symmetries detection for large-scale functions.