A Distributed Extension of the Turing Machine

The Turing Machine has two implicit properties that depend on its underlying notion of computing: the format is fully determinate and computations are information preserving. Distributed representations lack these properties and cannot be fully captured by Turing's standard model. To address this limitation a distributed extension of the Turing Machine is introduced in this paper. In the extended machine, functions and abstractions are expressed extensionally and computations are entropic. The machine is applied to the definition of an associative memory, with its corresponding memory register, recognition and retrieval operations. The memory is tested with an experiment for storing and recognizing hand written digits with satisfactory results. The experiment can be seen as a proof of concept that information can be stored and processed effectively in a highly distributed fashion using a symbolic but not fully determinate format. The new machine augments the symbolic mode of computing with consequences on the way Church Thesis is understood. The paper is concluded with a discussion of some implications of the extended machine for Artificial Intelligence and Cognition.