Interactive computation involves communication with the external world during the computation. This is in contrast to the traditional understanding of computation which assumes a simple interface between a computing agent and its environment, consisting in asking a question (input) and generating an answer (output).
The famous Church-Turing thesis attempts to define computation and computability in terms of Turing machines. However the Turing machine model only provides an answer to the question what computability of functions means and, with interactive tasks not always being reducible to functions, it fails to capture our broader intuition of computation and computability. While this fact has been admitted by Alan Turing himself, it was not until recently that the theoretical computer science community realized the necessity to define adequate mathematical models of interactive computation. Among the currently studied mathematical models of computation that attempt to capture interaction are Japaridze's hard- and easy-play machines elaborated within the framework of computability logic, Goldin's persistent Turing machines, Gurevich's abstract state machines.
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