Applications of Complex Network Dynamics in Ultrafast Electronics.

다국어 초록 (Multilingual Abstract)

The success of modern digital electronics relies on compartmentalizing logical functions into individual gates, and controlling their order of operations via a global clock. In the absence of such a timekeeping mechanism, systems of connected logic gates can quickly become chaotic and unpredictable -- exhibiting analog, asynchronous, autonomous dynamics. Such recurrent circuitry behaves in a manner more consistent with neural networks than digital computers, exchanging and conducting electricity as quickly as its hardware allows. These physics enable new forms of information processing that are faster and more complex than clocked digital circuitry. However, modern electronic design tools often fail to measure or predict the properties of large recurrent networks, and their presence can disrupt other clocked architectures.In this thesis, I study and apply the physics of complex networks of self-interacting logic gates at sub-ns timescales. At a high level, my unique contributions are: 1. I derive a general theory of network dynamics and develop open-source simulation libraries and experimental circuit designs to re-create this work; 2. I invent a best-in-class digital measurement system to experimentally analyze signals at the trillionth-of-a-second (ps) timescale; 3. I introduce a network computing architecture based on chaotic fractal dynamics, creating the first `physically unclonable function' with near-infinite entropy.In practice, I use a digital computer to reconfigure a tabletop electronic device containing millions of logic gates (a field-programmable gate array; FPGA) into a network of Boolean functions (a hybrid Boolean network; HBN). From within the FPGA, I release the HBN from initial conditions and measure the resulting state of the network over time. These data are transferred to an external computer and used to study the system experimentally and via a mathematical model.Existing mathematical theories and FPGA simulation tools produce incorrect results when predicting HBNs, and current FPGA-based measurement tools cannot reliably capture the ultrafast HBN dynamics. Thus I begin by generalizing prior mathematical models of Boolean networks in a way that reproduces extant models as limiting cases. Next I design a ps-scale digital measurement system (Waveform Capture Device; WCD). The WCD is an improvement to the state-of-the-art in FPGA measurement systems, having external application in e.g. medical imaging and particle physics. I validate the model and WCD independently, showing that they reproduce each-other in a self-consistent manner. I use the WCD to fit the model parameters and predict the behavior of simple HBNs on FPGAs.I go on to study chaotic HBN. I find that infinitesimal changes to the model parameters -- as well as uncontrollable manufacturing variations inherent to the FPGAs - cause near-identical HBNs to differ exponentially. The simulations predict that fractal patterns separate infinitesimally distinct networks over time, motivating the use of HBN dynamics as 'digital fingerprints' (Physically Unclonable Functions; PUFs) for hardware security. I conclude by rigorously analyzing the experimental properties of HBN-PUFs on FPGAs across a variety of statistical metrics, ultimately discovering super-exponential entropy scaling -- a significant improvement to the state-of-the-art.