Transcending the Limits of Turing Computability

Adamyan, Vadim A.; Calude, Cristian S.; Pavlov, Boris S.

Transcending the Limits of Turing Computability

Authors

Adamyan, Vadim A.

Calude, Cristian S.

Pavlov, Boris S.

Description

Hypercomputation or super-Turing computation is a ``computation'' that transcends the limit imposed by Turing's model of computability. The field still faces some basic questions, technical (can we mathematically and/or physically build a hypercomputer?), cognitive (can hypercomputers realize the AI dream?), philosophical (is thinking more than computing?). The aim of this paper is to address the question: can we mathematically build a hypercomputer? We will discuss the solutions of the Infinite Merchant Problem, a decision problem equivalent to the Halting Problem, based on results obtained in \cite{Coins,acp}. The accent will be on the new computational technique and results rather than formal proofs.
13 pages, 1 figure