The effect of severely tightening the uniformity of Boolean circuit families is investigated. The impact on NC and its subclasses is shown to depend on the characterization chosen for the class, while classes such as P appear to be more robust. Tightly uniform subclasses of NC whose separation may be within reach of current techniques emerge.

In this paper, we compare the saturation time scales for complexity, linear entropy and entanglement negativity two open quantum systems. Our first model is a coupled harmonic oscillator, where treat one of oscillators as bath. The second type Caldeira Leggett model, consider one-dimensional free scalar field Using these systems, discovered that both complexity purification from operator state ...

In this paper a low-power current-mode RMS-to-DC converter is proposed. The proposed converter includes absolute value circuit, squarer/divider circuit, low-pass filter and square root circuit which employ CMOS transistors operating in weak inversion region. The RMS-to-DC converter has low power consumption (<1μW), low supply voltage (0.9V), wide input range (from 50 nA to 500 nA), low relative...

Computational complexity is concerned with the complexity of solving problems and computing functions and not with the complexity of verifying circuit designs. The importance of formal circuit veriication is evident. Therefore, a framework of a complexity theory for formal circuit veriication with binary decision diagrams is developed. This theory is based on read-once projections. For many pro...

Many dynamic programming algorithms for discrete 0-1 optimization problems are just special (recursively constructed) tropical (min,+) or (max,+) circuits. A problem is homogeneous if all its feasible solutions have the same number of 1s. Jerrum and Snir [JACM 29 (1982), pp. 874– 897] proved that tropical circuit complexity of homogeneous problems coincides with the monotone arithmetic circuit ...

The idea of visual complexity, the history of its measurement, and its implications for behavior are reviewed, starting with structuralism and Gestalt psychology at the beginning of the 20th century and ending with visual complexity theory, perceptual learning theory, and neural circuit theory at the beginning of the 21st. Evidence is drawn from research on single forms, form and texture arrays...

The title of this paper highlights an emerging duality between two basic topics in algorithms and complexity theory. Algorithms for circuits refers to the design of algorithms which can analyze finite logical circuits or Boolean functions as input, checking a simple property about the complexity of the underlying function. For instance, an algorithm determining if a given logical circuit C has ...

The ability to measure the transcriptional response of cells has drawn much attention to the underlying transcriptional networks. To untangle the network, numerous models with corresponding reverse engineering methods have been applied. In this work, we propose a non-linear model with adjustable degrees of complexity. The corresponding reverse engineering method uses a probabilistic scheme to r...