Exact Graph Coloring for Functional Decomposition: Do We Need It?

Finding column multiplicity index is one of important component processes in functional decomposition of discrete functions for circuit design and especially Data Mining applications. How important it is to solve this problem exactly from the point of view of the minimum complexity of decomposition, and related to it error in Machine Learning type of applications? In order to investigate this problem we wrote two graph coloring programs: exact program EXOC and approximate program DOM (DOM cab give provably exact results on some types of graphs). These programs were next incorporated into the multi-valued decomposer of functions and relations NVGUD. Extensive testing of MVGUD with these programs has been performed on various kinds of data. Based on these tests we demonstrated that exact graph coloring is not necessary for high-quality functional decomposers, especially in Data Mining applications, giving thus another argument that efficient and effective Machine Learning approach based on decomposition is possible

Regularity and Symmetry as a Base for Efficient Realization of Reversible Logic Circuits

We introduce a Reversible Programmable Gate Array (RPGA) based on regular structure to realize binary functions in reversible logic. This structure, called a 2 * 2 Net Structure, allows for more efficient realization of symmetric functions than the methods shown by previous authors. In addition, it realizes many non-symmetric functions even without variable repetition. Our synthesis method to RPGAs allows to realize arbitrary symmetric function in a completely regular structure of reversible gates with smaller “garbage” than the previously presented papers. Because every Boolean function is symmetrizable by repeating input variables, our method is applicable to arbitrary multi-input, multi-output Boolean functions and realizes such arbitrary function in a circuit with a relatively small number of garbage gate outputs. The method can be also used in classical logic. Its advantages in terms of numbers of gates and inputs/outputs are especially seen for symmetric or incompletely specified functions with many outputs

Efficient suboptimal state assignment for large sequential machines

Optimal state assignment is one of the most important problems in the automatic synthesis of sequential machines. State assignment approaches can be divided into: Structural (that construct 'suboptimal' assignments) and statistical (that generate assignments). The author has developed and implemented a new structural method. Analyzing the factors that influence the quality of assignments and performing experiments, it is concluded that the distribution of solutions is close to a normal distribution. Some probabilistic quality measures for assignments and assignment methods are introduced and applied to the structural and random approach. Both approaches are compared and it is indicated that the difficulty in evaluating the quality of an assignment by statistical approach is the main reason why structural approaches can be more efficient than statistical ones

Full decomposition of sequential machines with the output behaviour realization

The control units of large digital systems can use up to 80% of the entire hardware implementing the system. Therefore, it is very important to reduce the amount of hardware taken by the control unit and to simplify the design, implementation and verification process. In most cases, the control unit can be constructed as a sequential machine. In this work, a general and unified classification of full-decompositions and formal definitions of different sorts of full-decompositions for Mealy and Moore machines are presented and some theorems about the existence of full-decompositions with the output behaviour realization are formulated and proved. This theorems constitute a theoretical basis for the practical decomposition algorithms and for the software system calculating different sorts of decomposition for sequential machines

Term Trees in Application to an Effective and Efficient ATPG for AND–EXOR and AND–OR Circuits

A compact data representation, in which the typically required operations are performed rapidly, and effective and efficient algorithms that work on these representations are the essential elements of a successful CAD tool. The objective of this paper is to present a new data representation—term trees (TTs)—and to discuss its application for an effective and efficient structural automatic test-pattern generation (ATPG). Term trees are decision diagrams similar to BDDs that are particularly suitable for structure representation of AND–OR and AND–EXOR circuits. In the paper, a flexible algorithm for minimum term-tree construction is discussed and an effective and efficient algorithm for ATPG for AND–EXOR and AND–OR circuits is proposed. The term trees can be used for many other purposes in logic design and in other areas—for all purposes where compact representation and efficient manipulation of term sets is important. The presented experimental results show that term trees are indeed a compact data representation allowing fast manipulations. They form a good base for algorithms considering the function’s and circuit’s term structures

Efficient suboptimal state assignment for large sequential machines

\u3cp\u3eOptimal state assignment is one of the most important problems in the automatic synthesis of sequential machines. State assignment approaches can be divided into: Structural (that construct 'suboptimal' assignments) and statistical (that generate assignments). The author has developed and implemented a new structural method. Analyzing the factors that influence the quality of assignments and performing experiments, it is concluded that the distribution of solutions is close to a normal distribution. Some probabilistic quality measures for assignments and assignment methods are introduced and applied to the structural and random approach. Both approaches are compared and it is indicated that the difficulty in evaluating the quality of an assignment by statistical approach is the main reason why structural approaches can be more efficient than statistical ones.\u3c/p\u3

Embedded computing technology for highly-demanding cyber-physical systems

\u3cp\u3eThe recent spectacular progress in the microelectronic, information, communication, material and sensor technologies created a big stimulus towards development of much more sophisticated, coherent and fit to use, smart communicating cyber-physical systems (CPS). The huge and rapidly developing markets of the modern CPS represent great opportunities for both private enterprises and country economies. However, these opportunities come with a price of unusual systems complexity, as well as, stringent and difficult to satisfy requirements of the modern CPS applications. Specifically, numerous mobile and autonomous CPS applications require a. o. a guaranteed (ultra-)high performance or (ultra-)low energy consumption, as well as, a high reliability, safety and security. To adequately address these problems and overcome the related challenges a sophisticated embedded computing and embedded design technologies are needed. After a brief introduction to modern CPS and consideration of several serious challenges of their design, this paper discusses the embedded computing technology needed for the modern complex and highly-demanding mobile and autonomous CPS.\u3c/p\u3