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Computational Completeness of Interaction Machines and Turing Machines

10 pagesPublished: June 22, 2012

Abstract

In the paper we prove in a new and simple way that Interaction
machines are more powerful than Turing machines. To do that
we extend the definition of Interaction machines to multiple interactive
components, where each component may perform simple computation.
The emerging expressiveness is due to the power of interaction and allows
to accept languages not accepted by Turing machines. The main
result that Interaction machines can accept arbitrary languages over a
given alphabet sheds a new light to the power of interaction. Despite of
that we do not claim that Interaction machines are complete. We claim
that a complete theory of computer science cannot exist and especially,
Turing machines or Interaction machines cannot be a complete model of
computation. However complete models of computation may and should
be approximated indefinitely and our contribution presents one of such
attempts.

Keyphrases: completeness, computation, expressiveness, Interaction machine, Turing machine

In: Andrei Voronkov (editor). Turing-100. The Alan Turing Centenary, vol 10, pages 405--414

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