A theory of interactive computation

Abstract

Many embedded systems behave very differently from classical machine models: they interact with an unpredictable environment, they are always on, and they change over time. This leads to the interesting question of what a computational theory of interactive, evolving programs should look like. While the behavior of such programs has been well-studied in concurrency theory, there has been much less emphasis on their computational aspects. A theory of interactive computation must necessarily lead beyond the classical, finitary models of computation. We describe a simple model of interactive computing consisting of one component C and an environment E, interacting using single streams of input and output signals and with a number of realistic conditions in effect. The model enables us to study the computational implications of interaction, building on the theory of ω-automata. Viewing components as interactive transducers, we show that the interactive capabilities of components for recognition and generation are equivalent. We also show that all interactively computable functions are limit-continuous and that interactively computable bijections have interactively computable inverses. The model elegantly characterizes interactive computation in a stream setting. © 2006 Springer-Verlag Berlin Heidelberg.