The overall goal of this project is to understand how to build smarter, more compact, and more environmentally friendly computing devices that can cope efficiently with uncertainty. Many current computer-based machines, for example, mobile phones and advanced biomedical devices, depend on remote data centers (the so-called cloud) to provide brain-like computational services that employ artificial intelligence and are probabilistic in nature. These centers consume enormous amounts of high-cost resources such as computer hardware, computing time, and electrical energy. Embedding their functions directly in low-cost, reliable and environmentally friendly ways in end-user devices like smartphones is a key research challenge with broad implications. One way of doing this is the stochastic computing (SC) approach explored in this project. The SC circuits are inherently probabilistic and are orders-of-magnitude smaller and more error-tolerant than conventional circuits. Thus, they provide novel ways to create tiny, low-cost and reliable systems. Besides its potential for reducing the cost of, and need for, large systems like data centers, SC has recently been shown suitable for extremely resource-restricted biomedical applications such as retinal implants to restore vision to the blind. The project will also enable graduate, undergraduate and underrepresented students to be trained in computing techniques at the forefront of modern computing technologies, thus contributing to the future workforce.<br/><br/>Traditional computer science is mostly devoted to non-probabilistic (deterministic) methods that, although far easier to understand than probabilistic, are less well-suited to the applications of interest cited above. Stochastic computing is one of the most promising probabilistic techniques available. It can be concisely defined as computing with probabilities encoded in randomized streams of 0?s and 1?s. It is readily implementable with standard electronic technology; for example, a single logic gate can perform multiplication, even when the input data is very noisy. The project will investigate the theoretical underpinnings of SC and its application to severely resource-restricted systems. Among the questions to be addressed are: What are the computational fundamental limits on SC?s accuracy? How can SC?s unique progressive precision and randomness properties be exploited? How can system architects efficiently balance accuracy, performance, energy needs, and overall system cost? Prototype systems will be designed and evaluated via mathematical analysis, simulation and emulation using field programmable gate arrays. These include designs incorporating neural networks, as well as smart cameras, medical implants, and portable automatic speech-recognition systems. The research is also expected to provide useful insights into other probabilistic technologies such as quantum computing.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.