Modelling interactive computing systems: Do we have a good theory of what computers are?

Computers are increasingly interactive. They are no more transformational systems producing a final output after a finite execution. Instead, they continuously react in time to external events that modify the course of computing execution. While philosophers have been interested in conceptualizing computers for a long time, they seem to have paid little attention to the specificities of interactive computing. We propose to tackle this issue by surveying the literature in theoretical computer science, where one can find explicit proposals for a model of interactive computing. In that field, the formal modelling of interactive computing systems has been brought down to whether the new interaction models are reducible to Turing Machines. There are three areas where interaction models are framed. The comparison between TMs and interactive system models is at stake in all of them. These areas are namely some works on concurrency by Milner, on Reactive Turing Machines, and on interaction as a new computing paradigm. For each of the three identified models, we present its motivation, sum up its account for interaction and its legacy, and point out issues regarding the understanding of computers. The survey shows difficulties for epistemologists. The reason is that these analyses focus on the formal equivalence between interactive models of computation and classic ones. Such a project is different from addressing how a computing machine can be interactive: in other words, which mechanisms allow it.