In this paper, we address the question of what current computers are from the point of view of human-computer interaction. In the early days of computing, the Turing machine (TM) has been the cornerstone of the understanding of computers. The TM defines what can be computed and how computation can be carried out. However, in the last decades, computers have evolved and increasingly become interactive systems, reacting in real-time to external events in an ongoing loop. We argue that the TM does not provide a mechanistic explanation for interactive computing. The reason is that the fundamental phenomena relevant to interactive computing are out of the scope of classical computability theory. Part of the explanatory power of the TM relies on what we propose to call an execution model. An execution model belongs to a level of abstraction where it is possible to describe both the functional architecture and the execution in mechanistic terms. An updated execution model is warranted to provide the minimal mechanistic description for interactive computation as a counterpart of what the TM could explain regarding Church-Turing computation. It would support an explanation of the ubiquitous computing devices we know -those interacting with humans, e.g., through digital interfaces. We show that such a model is not available within interactive models of computation and that relevant abstractions and concerns are available in computer engineering but need to be identified and gathered. To fill this void, we propose to reflect on the level of abstractionrequired to support the mechanistic description of an interactive execution and propose some preliminary requirements.

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Turing's work on computability served as the founding theoretical framework for computer science. It aimed at formalizing the intuitive notion of algorithm and gave birth to the concepts of logical automaton and abstract machine. The latter are used to evaluate the expressiveness of programming languages. However, current systems are difficult to model within an algorithmic framework and question the relevance of the classical model. The systems we know are indeed characterized by continuous interactions between human agents, physical and computational processes. Programming these interactive systems requires to specify causal relationships between processes, and not simply the execution of computation. In this paper, we propose to define an equivalent of the classical abstract machine, to model programmable interactive systems. Based on our distinction between computation programming and interaction programming and previous theoretical works that have questioned the classical framework, we elicit the minimal requirements of an abstract machine for interaction. This work is a fist step toward an interactive model to evaluate the expressivity of interaction-oriented languages. CCS CONCEPTS• Human-centered computing → HCI theory, concepts and models.