A New Approach to the Decomposition of Boolean Functions by the Method of q-Partitions. I. Separating Decomposition of Full and Partial Functions

A new approach to the decomposition of Boolean functions of n variables is considered; the functions being decomposed can be represented in various forms. The approach is based on the method of q-partitions of minterms and on the introduced concept of a decomposition clone. The theorem on simple separating decomposition of full and partial functions is formulated. The approach proposed is illustrated by examples.     

布尔函数的代数因子分解

本文改进了布尔函数的代数因子分解算法ALG_DIV和QF,采用“分治”方式降低了分解过程的计算时间复杂性,提高了多级逻辑函数分解的效率,能获得近似优化的多级逻辑分解结果.     

On Complexity of Computation of Partial Derivatives of Boolean Functions Realized by Zhegalkin Polynomials

The combinational complexity of a system of partial derivatives in the basis of linear functions is established for a Boolean function of n variables that is realized by a Zhegalkin polynomial. An algorithm whose complexity equals 3ⁿ – 2ⁿ modulo 2 additions is proposed for computation of all partial derivatives of such a function from the coefficients of its Zhegalkin polynomial.     

A new approach to the decomposition of Boolean functions by the method of <Emphasis Type="Italic">q</Emphasis>-partitions. III. Joint decomposition of a function system

The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean functions of variables specified in different representation forms. The approach is based on the method of q-partitions of conjuncterms and concept of decomposition clones. Theorems on joint decomposition of a system of full and partial functions are formulated. The approach is illustrated by examples. Parts I and II of this article are published in No. 5 (2001) and No. 1 (2002). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 39–58, March–April 2007.     

A New Method of Coding Minorants in Problems of Synthesis of Digital Devices from PLAs

A new method of coding minorants in decomposing a system of Boolean function is proposed. The method is based on the initial coding obtained from the minimal representation of the system in the so-called set-theoretical decomposition form obtained as a result of q-partitioning of conjuncterms of functions represented in DNF. A distinctive feature of the method is the preservation of the correspondence of the obtained codes of minorants to the block structure of the system being decomposed, which provides the minimum of informational capacity of PLAs.     

Noisy Image Decomposition: A New Structure,Texture and Noise Model Based on Local Adaptivity

These last few years, image decomposition algorithms have been proposed to split an image into two parts: the structures and the textures. These algorithms are not adapted to the case of noisy images because the textures are corrupted by noise. In this paper, we propose a new model which decomposes an image into three parts (structures, textures and noise) based on a local regularization scheme. We compare our results with the recent work of Aujol and Chambolle. We finish by giving another model which combines the advantages of the two previous ones.     

A new approach to the decomposition of boolean functions. 4. non-disjoint decomposition: the method of <Emphasis Type="Italic">p</Emphasis>, <Emphasis Type="Italic">q</Emphasis>-partitions

A set-theoretical approach to the non-disjoint decomposition of different forms of representation of Boolean functions of n variables is considered. This approach is based on the method of p,q-partitions of conjuncterms and on the concept of a decomposition clone. Two techniques of searching for some non-disjoint functional decomposition are described. Theorems on the non-disjoint decomposition of full and partial functions and their systems are formulated. The proposed approach is illustrated by examples. Parts I, II, and III of this article are published in No. 5 (2001), No. 1 (2002), and No. 2 (2007). Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 15-41, May–June 2009.     

A New Approach to the Gas Dynamics Equation: An Application of the Decomposition Method

The Adomian decomposition method is used to implement the homogeneous gas dynamics equations. The analytic solution of the equation is calculated in the form of a series with easily computable components. The homogeneous problem is quickly solved by observing the self-canceling "noise" terms whose sum vanishes in the limit. Comparing the methodology with some other known techniques shows that the present approach is effective and powerful. Many test modeling problems from mathematical physics, both linear and nonlinear are discussed to illustrate the effectiveness and the performance of the decomposition method.     

Responses of the reflectance indices PRI and NDVI to experimental warming and drought in European shrublands along a north-south climatic gradient

The aim of this study was to evaluate the use of ground-based canopy reflectance measurements to detect changes in physiology and structure of vegetation in response to experimental warming and drought treatment at six European shrublands located along a North-South climatic gradient. We measured canopy reflectance, effective green leaf area index (green LAIe) and chlorophyll fluorescence of dominant species. The treatment effects on green LAIe varied among sites. We calculated three reflectance indices: photochemical reflectance index PRI [531 nm; 570 nm], normalized difference vegetation index NDVI₆₈₀ [780 nm; 680 nm] using red spectral region, and NDVI₅₇₀ [780 nm; 570 nm] using the same green spectral region as PRI. All three reflectance indices were significantly related to green LAIe and were able to detect changes in shrubland vegetation among treatments. In general warming treatment increased PRI and drought treatment reduced NDVI values. The significant treatment effect on photochemical efficiency of plants detected with PRI could not be detected by fluorescence measurements. However, we found canopy level measured PRI to be very sensitive to soil reflectance properties especially in vegetation areas with low green LAIe. As both soil reflectance and LAI varied between northern and southern sites it is problematic to draw universal conclusions of climate-derived changes in all vegetation types based merely on PRI measurements. We propose that canopy level PRI measurements can be more useful in areas of dense vegetation and dark soils.