On algorithms and interaction

Abstract

Many IT-systems behave very differently from classical machine models: they interact with an unpredictable environment, they never terminate, and their behavior changes over time. Wegner [25,26] (see also [28]) recently argued that the power of interaction goes beyond the Church-Turing thesis. To explore interaction from a computational viewpoint, we describe a generic model of an 'interactive machine' which interacts with the environment using single streams of input and output signals over a simple alphabet. The model uses ingredients from the theory of w-automata. Viewing the interactive machines as transducers of infinite streams of signals, we show that their interactive recognition and generation capabilities are identical. It is also shown that, in the given model, all interactively computable functions are limit-continuous.