When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, system software, and programming language compilers or their runtime systems can trade deviations from correct behavior for lower resource usage. We present, for the first time, a synthesis of research results on computing systems that only make as many errors as their end-to-end applications can tolerate. The results span the disciplines of computer-aided design of circuits, digital system design, computer architecture, programming languages, operating systems, and information theory. Rather than over-provisioning the resources controlled by each of these layers of abstraction to avoid errors, it can be more efficient to exploit the masking of errors occurring at one layer and thereby prevent those errors from propagating to a higher layer.

We demonstrate the potential benefits of end-to-end approaches using two illustrative examples. We introduce a formalization of terminology that allows us to present a coherent view across the techniques traditionally used by different research communities in their individual layer of focus. Using this formalization, we survey tradeoffs for individual layers of computing systems at the circuit, architecture, operating system, and programming language levels as well as fundamental information-theoretic limits to tradeoffs between resource usage and correctness.