A Distributed Extension of the Turing Machine
This work addresses a foundational problem in computing theory by extending the Turing Machine to handle distributed representations, with implications for AI and cognition, though it appears incremental as an extension rather than a new paradigm.
The paper tackles the limitation of the Turing Machine in capturing distributed representations by introducing a distributed extension that uses extensional functions and entropic computations, applied to an associative memory for storing and recognizing handwritten digits with satisfactory results.
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.