A macroscopic structure was analyzed for a system comprising multiple elements in which the dynamics is affected by their distribution. First, a nonlinear Boltzmann equation, which has an integration term with respect to the distribution of the elements, was derived. Next, the moment vector equation (MVE) for the Boltzmann equation was derived. The average probability density function (pdf) in a steady state was derived using eigen analysis of the coefficient matrix of the MVE. The macroscopic structure of the system and the mechanism that provides the average pdf and the transient response were then analyzed using eigen analysis. Evaluation of the average pdf and transient response showed that using eigen analysis is effective for analyzing not only the transient and stationary properties of the system but also the macroscopic structure and the mechanism providing the properties.

Multihigh-dimensional chaotic systems were reduced to low-dimensional space embedded equations (SEEs), and their macroscopic and statistical properties were investigated using eigen analysis of the moment vector equation (MVE) of the SEE. First, the state space of the target system was discretized into a finite discrete space. Next, an embedding from the discrete space to a low-dimensional discrete space was defined. The SEE of the target system was derived using the embedding. Finally, eigen analysis was applied to the MVE of the SEE to derive the properties of the target system. The geometric increase in the dimension of the MVE with the dimension of the target system was avoided by using the SEE. The pdfs of arbitrary elements in the target nonlinear system were derived without a reduction in accuracy due to dimension reduction. Moreover, since the dynamics of the system were expressed by the eigenvalues of the MVE, it was possible to identify multiple steady states that cannot be done using numerical simulation. This approach can thus be used to analyze the macroscopic and statistical properties of multi-dimensional chaotic systems.

A method was developed for analyzing a system comprised of identical and indistinguishable elements with nonlinear dynamics. First, a moment vector equation (MVE) for the system was derived so as to avoid the curse of dimensionality by using the property that the elements are identical and indistinguishable. Next, an algorithm was developed to solve the MVE for deriving the moment vector in a steady state. It effectively uses eigen analysis on the basis of the property of the MVE. It can thus be used to clarify the structure of the solutions in the moment vector space and to derive multiple solutions by setting the initial value to the moment vector orthogonal to the solutions already obtained. Finally, the probability density function (pdf) for the state of the system was derived using the moment vectors in a steady state. Comparison of the pdfs thereby derived with those derived using numerical simulation showed that the method provided good approximations of the pdfs. Moreover, multiple solutions that are difficult to do using numerical simulation were derived.

In this paper, we describe a verification environment which is based on a constrained random layered testbench using SystemVerilog OOP. As SystemVerilog OOP technique does not allow multiple inheritance, we adopt SystemC to design components of a verification environment which employ multiple inheritance. Then SystemC design unit is linked to a SystemVerilog-based verification environment using SystemVerilog DPI and ModelSim macro. Employing multiple inheritance of SystemC makes the design phase of verification environment simple and easy through source code reusability without corruption due to multi-level single inheritance.

A method was developed for deriving the control input for a multi-dimensional discrete-time nonlinear system so that a performance index is approximately minimized. First, a moment vector equation (MVE) is derived; it is a multi-dimensional linear equation that approximates a nonlinear system in the whole domain of the system state and control input. Next, the performance index is approximated by using a quadratic form with respect to the moment vector. On the basis of the MVE and the quadratic form, an approximate optimal controller is derived by solving the linear quadratic optimal control problem. A bilinear optimal control problem and a mountain-car problem were solved using this method, and the solutions were nearly optimal.

Checker synthesis for assertion based verification becomes popular because of the recent progress on the FPGA prototyping environment. In the paper, we propose a checker synthesis method based on the finite input-memory automaton suitable for embedded RAM modules in FPGA. There are more than 1 Mbit memories in medium size FPGA's and such embedded memory cells have the capability to be used as the shift registers. The main idea is to construct a checker circuit using the finite input-memory automata and implement shift register chain by logic elements or embedded RAM modules. When using RAM module, the method does not consume any logic element for storing the value. Note that the shift register chain of input memory can be shared with different assertions and we can reduce the hardware resource significantly. We have checked the effectiveness of the proposed method using several assertions.

In this work, a novel Multiple Valued Exclusive-Or Sum Of Products (MVESOP) minimization formulation is analyzed and an algorithm is presented that detects minimum MVESOP expressions when the weight of the function is less than eight. A heuristic MVESOP algorithm based on a novel cube transformation operation is then presented. Experimental results on MCNC benchmarks and randomly generated functions indicate that the algorithm matches or outperforms the quality of the state of the art in ESOP minimizers.