This paper gives insight on Christiphor Crnilovich's multilayered and valuable painting art, lectures and ethnographic work, along with his biography. Within context of psycho-social environment in which Crnilovich has lived and created, as well as within context of this environment's relation towards an artist and a researcher, motivation of his local nickname "Kica Pustood" is being analysed.

Error-correcting decision diagrams [3] are a new method of providing fault-tolerance into logic circuits. By combining decision diagrams, which are an efficient way of representing switching functions, and error-correcting codes to obtain error-correcting decision diagrams, fault-tolerance is introduced already to the representations of switching functions. Depending on the technology, the implementation of these diagrams is straightforward and the obtained diagrams directly determine the layout of the final circuit. Thus, error-correcting decision diagrams are efficient robust representations of functions and require no additional checker circuitry when implemented on the circuit level. In this paper, we introduce error-correcting decision diagrams for multiple-valued functions and analyze their fault-tolerance. We consider error-correcting decision diagrams for multiple-valued functions generated with codes in the Hamming and the Lee metric. The fault-tolerance analysis shows that the robust diagrams have a significantly higher probability of correct outputs than corresponding non-redundant diagrams, while better error-correcting properties increase the complexity of the designs. However, we demonstrate that even with moderate increments in complexity it is possible to obtain significantly increased probabilities of correct outputs.

In this paper we examine the relationship between multiple-valued bent functions and Vilenkin-Chrestenson spectral invariant operations and Vilenkin-Chrestenson decision diagrams. In binary domain bent functions are a class of discrete functions with a highest degree of nonlinearity and form an essential part of cryptographic systems. Multiple-valued bent functions are an extension of bent functions to higher order finite fields. These functions are defined in terms of properties of their Vilenkin-Chrestenson spectra. We demonstrate that the application of spectral invariant operations to a given multiple-valued bent function does not alter the structure of the corresponding Vilenkin-Chrestenson decision diagrams. We exploit this property to efficiently represent whole sets of multiple-valued bent functions using a single Vilenkin-Chrestenson decision diagram. Furthermore, we present a decision diagram based method of construction of multiple-valued bent functions of arbitrary size.

The paper studies ternary logic functions that have decision diagrams of identical shape. The concept of beads, a special class of binary sequences, is extended to ternary sequences and are used to describe the shape of the decision diagrams representing functions that are mathematical models of such sequences. We point out that establishing the links between beads, functions, and their decision diagram representations can be useful in classification of ternary functions, checking the equivalence of functions, as well as their circuit implementations.

Beads are a particular class of binary sequences with interesting properties due to which they can be related to Binary decision diagrams. Recently, the concept of beads was extended to integer sequences and sequences over finite fields and used in the classification of logic functions in terms of decision diagrams. In this paper, sets of beads and integer beads are used to estimate the equality of structure of digital systems implementing logic functions.

The Fourier transform is a classical method in mathematical modeling of systems. Assuming finite non-Abelian groups as the underlying mathematical structure might bring advantages in modeling certain systems often met in computer science and information technologies. Frequent computing of the inverse Fourier transform is usually required in dealing with such systems. These computations require for each function value to compute many times traces of certain matrices. These matrices are products of matrix-valued entries of unitary irreducible representations and matrix-valued Fourier coefficients. In the case of large non-Abelian groups the complexity of these computations can be a limiting factor in applications. In this paper, we present a method for speeding-up computing the traces by using decision diagrams to operate on matrix-valued group representations and related Fourier coefficients.

Decision diagrams are an efficient way of representing switching functions and they are easily mapped to technology. A layout of a circuit is directly determined by the shape and the complexity of the decision diagram. By combining the theory of error-correcting codes with decision diagrams, it is possible to form robust circuit layouts, which can detect and correct errors. The method of constructing robust decision diagrams is analogous to the decoding process of linear codes, and is based on simple matrix and look-up operations. In this paper, the performance of robust binary decision diagrams is analyzed by determining the error probabilities for such constructions. Depending on the error-correcting properties of the code used in the construction, the error probability of a circuit can be significantly decreased by a robust decision diagram.

The paper studies binary and ternary functions that have decision diagrams of identical shape in the original and spectral (Fourier) domain. These functions are called Fourier-sweet functions. This class of functions involves certain classes of bent functions and quadratic forms in both binary and ternary cases. Bent functions and quadratic forms have applications in cryptography and error-correcting codes. Not all bent functions are Fourier-sweet functions. It follows, that Fourier-sweet functions are capable of capturing the differences among the classes of bent functions, and at the same time link them to quadratic forms. Representation by shape invariant decision diagrams in the original and spectral domain might provide some better insight into features of bent functions and quadratic forms. The functions represented by the disjoint quadratic forms in the binary case and diagonal forms in the ternary case are elementary Fourier-sweet functions. In both binary and ternary cases, the application of affine transformations, under certain precisely specified restrictions, to the elementary Fourier-sweet functions produces other Fourier-sweet functions.

Bent functions are a class of discrete functions which exhibit the highest degree of nonlinearity. As such bent functions form an essential part of cryptographic systems. Original concept of bent functions defined in GF(2) can be extended to multiple-valued case. Multiple-valued bent functions are defined in therms of properties of their Vilenkin-Chrestenson spectra. Decision diagrams are a method of compact representation of discrete functions. Special types of decision diagrams have been introduced for various types of discrete functions. In this paper we demonstrate how Vilenkin-Chrestenson decision diagrams can be used for efficient representation of multiple-valued bent functions.

Decision diagrams are an efficient way of representing switching functions and they are easily mapped to technology. The layout of a circuit is directly determined by the shape of the decision diagram. By combining the theory of error-correcting codes with decision diagrams, it is possible to form robust circuit layouts, which can detect and correct errors. The method of constructing robust decision diagrams is analogous to the decoding process of linear codes, and can be based on simple matrix and look-up operations. In this paper, we focus on error-correcting decision diagrams for multiple-valued functions, considering them for both the Hamming metric and the Lee metric. The performance of robust decision diagrams is analyzed by determining the error probabilities for such constructions. Depending on the error-correcting properties of the code used in the construction, the error probability of a circuit can be significantly decreased by a robust decision diagram.

The construction of modern cryptographic systems relies on the so-called resilient Boolean functions, a special class of Boolean functions that possesses a balance between a high level of nonlinearity and correlation immunity. In this paper, we discuss the problem of the compact representation and efficient construction of resilient functions. Binary Decision Diagrams (BDDs) were extensively used as a method of compact representation of various classes of Boolean functions. Furthermore, BDDs offer an opportunity for the efficient implementation of different construction methods for resilient functions. In this paper, we make use of BDDs with attributed edges to provide an implementation of two construction methods proposed by Maitra and Sakar. In addition, we demonstrate that the size of BDDs of resilient functions obtained in this way grows linearly with the number of variables.

Spectral techniques on Abelian groups are a well-established tool in diverse fields such as signal processing, switching theory, multi-valued logic and logic design. The harmonic analysis on finite non-Abelian groups is an extension of them, which has also found applications for particular tasks in the same fields. It takes advantages of the peculiar features of the domain groups and their dual objects. Representing unitary irreducible representations, that are kernels of Fourier transforms on non-Abelian groups, in a compact manner is a key task in this area. These representations are usually specified in terms of rectangular matrices with matrix entries. Therefore, the problem of their efficient representations can be viewed as handling large rectangular matrices with matrix-valued entries. Quantum Multiple-valued Decision Diagrams (QMDDs) and Heterogeneous Decision Diagrams (HDDs) have been used for representation of matrices with numerical values, under some restrictions to the order of matrices to be represented. In this paper, we present a generalization of this concept for the representation of rectangular matrices with matrix-valued entries. We also demonstrate an implementation of an XML-based software package aimed at handling such data structures.

Decision diagrams are an efficient way of representing switching functions and they are easily mapped to technology. A layout of a circuit is directly determined by the shape and the complexity of the decision diagram. By combining the theory of error-correcting codes with decision diagrams, it is possible to form robust circuit layouts, which can detect and correct errors. The method presented in this paper is analogous to the decoding process of linear codes, and is based on simple matrix and look-up operations.

Field programmable gate arrays (FPGAs) are a useful tool for rapid prototyping as well as for small volume production of logic circuits. The use of Quaternary Decision Diagrams has been proposed as an efficient method for developing FPGA based solutions. The recently introduced Xilinx Virtex-5 family, is based around six input LUTs. Therefore, Quaternary Decision Diagrams are especially suited for the description of circuits implemented by this family.In this paper we present a system capable of developing FPGA implementations of switching functions using Quaternary Decision Diagrams, with the Virtex-5 family in focus. The proposed method is based on XML framework for representation of decision diagrams.

(francuski) La région de Vlasotince s'étend sur le territoire des bassins central et inférieur de la rivière Vlasina au Sud-Est de la Serbie. Les contrées nord de Vlasotince côtoient le Zaplanje; celles de l'Est s'étendent jusqu'a la Luznica; celles du Sud côtoient la région de Crna Trava et la région de Vlasina, ainsi que celle de Predejane et celle de Grdelica; tandis que les contrées ouest donnent sur la région de Leskovac. Sur le territoire de Vlasotince se rencontrent tous les trois parlers de Prizren et du Timok: le parler de Luznica, le parler de Zaplanje et le parler sud-moravien. Les premières recherches du parler de la région de Vlasotince (O. Broch 1903; A. Belic 1905) ont définitivement démontre qu'il faudrait consacrer des recherches particulières a une différenciation intérieure des sous-dialectes de Prizren et du Timok sur le terrain de Vlasotince. C'est ce qu'ont aussi indique les résultats des recherches ultérieures de l'espace dialectal de Vlasotince (S. Stankovic 1994; 1997). Dans la présente recherche, les frontières sous-dialectales, définies par Belic, des parlers de Prizren et du Timok dans la partie de Vlasotince de la Serbie du Sud-Est sont précisées et présentées avec des modifications sur la carte linguistique réduite. Les matériaux dialectaux rassembles ont aide a déterminer la frontière est du parler de Zaplanje sur le terrain de Vlasotince-qui est enmeme temps la frontiere ouest du parler de Luznica- a partir de l'embouchure de la rivière Tegosnica dans la rivière Vlasina, et englobant les villages Tegosnica et Stranjevo. Cette frontière longe la rive droite de Vlasina, elle passe par le village Gornji Ora et le village Aleksine jusqu'au village Svodje, et ensuite elle se détourne en direction du Nord en laissant le village Borin Dol sur la cote ouest; de la elle continue a longer la rive gauche de Pusta reka et elle surgit, entre le village Zavidince d'un cote et deux villages nommes Prisjan de l'autre, dans le village Gornje Zaplanje. La frontière ouest de l'idiome de Zaplanje - représentant a la fois la frontière est du parler sud-moravien - part de la source de la rivière Bistrica au Sud, puis longeant la rivière Rastovnica, a l'Est du village Ramna Gora, cette frontiere descend brusquement dans la vallée de Vlasina, d'ou elle se dirige vers le Nord en suivant la ligne Krusevica -Crnatovo - Gornja Lomnica - Sredor - Gunjetina et elle débouche a Gornje Zaplanje, a l'Ouest de l'agglomération Komarica.

Distinction between behavioral and structural models is one of the key points in high-level synthesis and modern hardware design. Decision Diagrams are know to be an efficient way of representation of switching functions. In recent years they have become very important tool in fields of logic designs for the tasks of logic circuit design, testing and verification. Correspondence between decision diagrams and structural hardware models is well known. On other hand decision diagrams can be easily converted into high level formal language branching programs, which can be viewed as behavioral system models. The ability to freely flow between these two modeling strategies illustrates the versatility of decision diagrams as a form of representation. In this paper, we explore the relationship of recently introduced [30], [29] XML based system for representation of Decision Diagrams with notions of behavioral and structural models. We examine this problem on example of automatic synthesis of branching programs. A large number of systems for manipulation of decision diagrams has been proposed over the years. In our previous work we have proposed an XML based system for representation of various types of decision diagrams. This system was designed with robustness and flexibility in mind, permitting easy conversion of an abstract general decision diagram representation to application specific tasks. We further expand these properties of the systems by introducing an extension that is capable of automatic generation of branching programs in C/C++ structure, based on given discrete functions.