Publications
Chaogates Morphing logic gates that exploit dynamical patterns. Chaotic systems can yield a wide variety of patterns. Here we use this feature to generate all possible fundamental logic gate functions. This forms the basis of the design of a dynamical computing device, a chaogate, that can be rapidly morphed to become any desired logic gate. Here we review the basic concepts underlying this and present an extension of the formalism to include asymmetric logic functions. 

Reliable Logic Circuit Elements that Exploit Nonlinearity in the Presence of a Noise Floor. The response of a noisy nonlinear system to deterministic input signals can be enhanced by cooperative phenomena. We show that when one presents two square waves as input to a twostate system, the response of the system can produce a logical output (NOR=OR) with a probability controlled by the noise intensity. As one increases the noise (for fixed threshold or nonlinearity), the probability of the output reflecting a NOR=OR operation increases to unity and then decreases. Changing the nonlinearity (or the thresholds) of the system changes the output into another logic operation (NAND=AND) whose probability displays analogous behavior. The interplay of nonlinearity and noise can yield logic behavior, and the emergent outcome of such systems is a logic gate. This ”logical stochastic resonance” is demonstrated via an experimental realization of a twostate system with two (adjustable) thresholds. 

Realization of reliable and flexible logic gates using noisy nonlinear circuits. It was shown recently [Murali et al., Phys. Rev. Lett. 102, 10410 (2009)] that when one presents two square waves as input to a twostate system, the response of the system can produce a logical output (NOR/OR) with a probability controlled by the interplay between the system noise and the nonlinearity (that characterizes the bistable dynamics). One can switch or “morph” the output into another logic operation (NAND/AND) whose probability displays analogous behavior; the switching is accomplished via a controlled symmetrybreaking dc input. Thus, the interplay of nonlinearity and noise yields flexible and reliable logic behavior, and the natural outcome is, effectively, a logic gate. This “logical stochastic resonance” is demonstrated here via a circuit implementation using a linear resistor, a linear capacitor and four CMOStransistors with a battery to produce a cubiclike nonlinearity. This circuit is simple, robust, and capable of operating in very high frequency regimes; further, its ease of implementation with integrated circuits and nanoelectronic devices should prove very useful in the context of reliable logic gate implementation in the presence of circuit noise. 

A NoiseAssisted Reprogrammable Nanomechanical Logic Gate. We present a nanomechanical device, operating as a reprogrammable logic gate, and performing fundamental logic functions such as AND/OR and NAND/NOR. The logic function can be programmed (e.g., from AND to OR) dynamically, by adjusting the resonator’s operating parameters. The device can access one of two stable steady states, according to a specific logic function; this operation is mediated by the noise floor which can be directly adjusted, or dynamically “tuned” via an adjustment of the underlying nonlinearity of the resonator, i.e., it is not necessary to have direct control over the noise floor. The demonstration of this reprogrammable nanomechanical logic gate affords a path to the practical realization of a new generation of mechanical computers. 

Logical stochastic resonance. In a recent publication it was shown that, when one drives a twostate system with two square waves as input, the response of the system mirrors a logical output (NOR/OR). The probability of obtaining the cor rect logic response is controlled by the interplay between the noisefloor and the nonlinearity. As one increases the noise intensity, the probability of the output reflecting a NOR/OR operation increases to unity and then decreases. Varying the nonlinearity (or the thresholds) of the system allows one to morph the output into another logic operation (NAND/AND) whose probability displays analogous behavior. Thus, the outcome of the interplay of nonlinearity and noise is a flexible logic gate with enhanced perfor mance. Here we review this concept of ”Logical Stochastic Resonance” (LSR) and provide details of an electronic circuit system demonstrating LSR. Our proofofprinciple experiment involves a particularly simple realization of a twostate system realized by two adjustable thresholds. We also review CMOS implementations of a simple LSR circuit, and the concatenation of these LSR modules to emulate combi national logic, such as data flipflop and full adder operations. 

Logic from nonlinear dynamical evolution. We propose a direct and flexible implementation of logic operations using the dynamical evolution of a nonlinear system. The concept involves the observation of the state of the system at different times to obtain different logic outputs. We explicitly implement the basic NAND, AND, NOR, OR and XOR logic gates, as well as multipleinput XOR and XNOR logic gates. Further we demonstrate how the single dynamical system can do more complex operations such as bitbybit addition in just a few iterations. 

Exploiting Nonlinear Dymanics to Store and Process Information. By applying nonlinear dynamics to the dense storage of information, we demonstrate how a single nonlinear dynamical element can store M items, where M is variable and can be large. This provides the capability for naturally storing data in different bases or in different alphabets and can be used to implement multilevel logic. Further we show how this method of storing information can serve as a preprocessing tool for (exact or inexact) pattern matching searches. Since our scheme involves just a single procedural step, it is naturally set up for parallel imple mentation and can be realized with hardware currently employed for chaosbased computing architectures. 

Creating morphable logic gates using logical stochastic resonance in an engineered gene network. The idea of Logical Stochastic Resonance is adapted and applied to an autoregulatory gene network in the bacteriophage λ. This biological logic gate can emulate or morph the AND and OR gates, through varying internal system parameters, in a noisy background. Such logic gates afford intriguing possibilities in the realization of engineered genetic networks, in which the function of the gate can be changed after the network has been assembled: this allows a single gene network to be used for many different applications in the emerging field of synthetic biology. 
Presentations
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