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Logical Stochastic Resonance


The density of computing elements like transistors has increased steadily over the last few decades in accordance with the Moore’s law. As computational devices and platforms continue to shrink in size and increase in speed, we are increasingly encountering fundamental noise characteristics that cannot be suppressed or eliminated.
In dynamical systems, noise and nonlinearity can cooperate to produce novel and counterintuitive effects like Stochastic Resonance (SR), which implies enhancement of a signal with aid of noise. Hence, an understanding of the cooperative behavior between a device noise floor and its nonlinearity is bound to play an increasingly crucial, even essential role in the design and development of future computational concepts and devices. In our research, we have found that the response of a simple threshold detector to input signals, consisting of two random square waves, in an optimal band of noise, is a logical combination of the two input signals. That is, a nonlinear system and noise can implement a logic function on inputs. This phenomenon has been dubbed as Logical Stochastic Resonance.

The underlying principle is fairly simple. Consider a general nonlinear dynamic system, given by ?????, where F(x) is a generic nonlinear function giving rise to a potential with two distinct energy wells. I is a low amplitude input signal and ??? is an additive zero-mean Gaussian noise with unit variance, D being the noise strength. A logical input-output correspondence is achieved by encoding N inputs in N square waves. Specifically, for two logic inputs, we drive the system with a low amplitude signal I, taken to be the sum of two trains of aperiodic pulses encoding the two logic inputs. The logic inputs can be either 0 or 1, giving rise to 4 distinct logic input sets: (0, 0), (0, 1), (1, 0), and (1, 1). The input signal I, generated by adding two independent input signals, is a three-level aperiodic waveform.
The output of the system is determined by its state; e.g., the output can be considered a logical 1 if it is in one well, and logical 0 if its in the other. Hence, when the system switches wells, the output is ‘‘toggled”.
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The above fig shows the response of system x(t) for noise intensities D equal to 0.01, 0.5 and 1 for a piece wise linear function f(x). A reliable OR/NOR gate (center panel) is obtained only for optimal noise. That is both low noise or high noise result in degradation of performance.