There are several attempts to generate chaotic binary sequences by using one-dimensional maps. From the standpoint of engineering applications, it is necessary to evaluate statistical properties of sample sequences of finite length. In this paper we attempt to evaluate the statistics of chaotic binary sequences of finite length. The large deviation theory for dynamical systems is useful for investigating this problem.

A merged analog-digital circuit architecture is proposed for implementing intelligence in SoC systems. Pulse modulation signals are introduced for time-domain massively parallel analog signal processing, and also for interfacing analog and digital worlds naturally within the SoC VLSI chip. Principles and applications of pulse-domain linear arithmetic processing are explored, and the results are expanded to the nonlinear signal processing, including an arbitrary chaos generation and continuous-time dynamical systems with nonlinear oscillation. Silicon implementations of the circuits employing the proposed architecture are fully described.

It is well known that the Hopfield Model (HM) for neural networks to solve the TSP suffers from three major drawbacks: (D1) it can converge to non-optimal local minimum solutions; (D2) it can also converge to non-feasible solutions; (D3) results are very sensitive to the careful tuning of its parameters. A number of methods have been proposed to overcome (D1) well. In contrast, work on (D2) and (D3) has not been sufficient; techniques have not been generalized to larger classes of optimization problems with constraint including the TSP. We first construct Extended HMs (E-HMs) that overcome both (D2) and (D3). The extension of the E-HM lies in the addition of a synapse dynamical system cooperated with the corrent HM unit dynamical system. It is this synapse dynamical system that makes the TSP constraint hold at any final states for whatever choices of the HM parameters and an initial state. We then generalize the E-HM further into a network that can solve a larger class of continuous optimization problems with a constraint equation where both of the objective function and the constraint function are non-negative and continuously differentiable.