On the complexity of dynamic tests for logic functions

A generalization of the concept of dynamic test is proposed for detecting logic and parametric faults at input / output terminals of logic networks realizing k— valued logic functions (k > 2). Upper and lower bounds on the complexity (i.e., length) of minimal dynamic tests are obtained for various classes of logic functions

Complementary Symmetry Nanowire Logic Circuits: Experimental Demonstrations and in Silico Optimizations

Complementary symmetry (CS) Boolean logic utilizes both p- and n-type field-effect transistors (FETs) so that an input logic voltage signal will turn one or more p- or n-type FETs on, while turning an equal number of n- or p-type FETs off. The voltage powering the circuit is prevented from having a direct pathway to ground, making the circuit energy efficient. CS circuits are thus attractive for nanowire logic, although they are challenging to implement. CS logic requires a relatively large number of FETs per logic gate, the output logic levels must be fully restored to the input logic voltage level, and the logic gates must exhibit high gain and robust noise margins. We report on CS logic circuits constructed from arrays of 16 nm wide silicon nanowires. Gates up to a complexity of an XOR gate (6 p-FETs and 6 n-FETs) containing multiple nanowires per transistor exhibit signal restoration and can drive other logic gates, implying that large scale logic can be implemented using nanowires. In silico modeling of CS inverters, using experimentally derived look-up tables of individual FET properties, is utilized to provide feedback for optimizing the device fabrication process. Based upon this feedback, CS inverters with a gain approaching 50 and robust noise margins are demonstrated. Single nanowire-based logic gates are also demonstrated, but are found to exhibit significant device-to-device fluctuations

Combining Linear Logic and Size Types for Implicit Complexity

Several type systems have been proposed to statically control the time complexity of lambda-calculus programs and characterize complexity classes such as FPTIME or FEXPTIME. A first line of research stems from linear logic and restricted versions of its !-modality controlling duplication. A second approach relies on the idea of tracking the size increase between input and output, and together with a restricted recursion scheme, to deduce time complexity bounds. However both approaches suffer from limitations : either a limited intensional expressivity, or linearity restrictions. In the present work we incorporate both approaches into a common type system, in order to overcome their respective constraints. Our system is based on elementary linear logic combined with linear size types, called sEAL, and leads to characterizations of the complexity classes FPTIME and 2k-FEXPTIME, for k >= 0

Performing optical logic operations by a diffractive neural network

Optical logic operations lie at the heart of optical computing, and they enable many applications such as ultrahigh-speed information processing. However, the reported optical logic gates rely heavily on the precise control of input light signals, including their phase difference, polarization, and intensity and the size of the incident beams. Due to the complexity and difficulty in these precise controls, the two output optical logic states may suffer from an inherent instability and a low contrast ratio of intensity. Moreover, the miniaturization of optical logic gates becomes difficult if the extra bulky apparatus for these controls is considered. As such, it is desirable to get rid of these complicated controls and to achieve full logic functionality in a compact photonic system. Such a goal remains challenging. Here, we introduce a simple yet universal design strategy, capable of using plane waves as the incident signal, to perform optical logic operations via a diffractive neural network. Physically, the incident plane wave is first spatially encoded by a specific logic operation at the input layer and further decoded through the hidden layers, namely, a compound Huygens’ metasurface. That is, the judiciously designed metasurface scatters the encoded light into one of two small designated areas at the output layer, which provides the information of output logic states. Importantly, after training of the diffractive neural network, all seven basic types of optical logic operations can be realized by the same metasurface. As a conceptual illustration, three logic operations (NOT, OR, and AND) are experimentally demonstrated at microwave frequencies

A Study of Membership Functions on Mamdani-Type Fuzzy Inference System for Industrial Decision-Making

The complexity of product design in industry has been continuously increasing. More factors are required to be taken into account simultaneously before a decision about the new product could be determined. For this reason, decision-making process costs much more time and it may even be impossible to determine the optimal decision by normal calculations. Therefore, Fuzzy Inference System based on Fuzzy Logic is introduced as a quick decision-making tool to arrive at a good decision within much shorter time.This thesis focuses on studying the features of membership functions in Mamdani-type fuzzy inference process. It is aimed at making the black box of fuzzy inference system to be transparent by adjusting the membership functions to control the relations between input and output variables. Systematic trial and error is implemented based on the Fuzzy Logic Toolbox from MATLAB, and conclusions developed from experiments help eliminate the uncertainties of membership functions, so that the inference process turns to be more precise and reliable. Firstly, Single-Input Single-Output (SISO) Fuzzy Inference System is discussed through the adjustment of membership functions, and the influence on input-output relations are concluded. Next, Two-Input Single-Output (TISO) Fuzzy Inference System is simulated to verify the conclusions from SISO Fuzzy Inference System, and general features of membership functions on affecting input-output relation are developed. Then, an approach using weights on input variables, for practical decision-making process, is derived. Finally, a design problem of timing system of automobile engine is chosen as case study to examine the validity of conclusions on practical decision-making problem

Fuzzy Logic System for Slope Stability Prediction

The main goal of this research is to predict the stability of slopes using fuzzy logic system. GeoStudio, a commercially available software was used to compute safety factors for various designs of slope. The general formulation of the software could analyze slope stability using various methods of analysis i.e. Morgenstern-Price, Janbu, Bishop and Ordinary to calculate the safety factors. After analyzing, fuzzy logic was used to predict the slope stability. Fuzzy logic is based on natural language and conceptually easy to understand, flexible, tolerant of imprecise data and able to model nonlinear functions of arbitrary complexity. Several important parameters such as height of slope, unit weight of slope material, angle of slope, coefficient of cohesion and internal angle of friction were used as the input parameters, while the factor of safety was the output parameter. A model to test the stability of the slope was generated from the calculated data. This model presented a relationship between input parameters and stability of the slopes. Results showed that the prediction using fuzzy logic was accurate and close to the target data

Towards Biochemical Filter with Sigmoidal Response to pH Changes: Buffered Biocatalytic Signal Transduction

We realize a biochemical filtering process by introducing a buffer in a biocatalytic signal-transduction logic system based on the function of an enzyme, esterase. The input, ethyl butyrate, is converted into butyric acid-the output signal, which in turn is measured by the drop in the pH value. The developed approach offers a versatile "network element" for increasing the complexity of biochemical information processing systems. Evaluation of an optimal regime for quality filtering is accomplished in the framework of a kinetic rate-equation model.Comment: PDF, 23 page