Transcending the Limits of Turing Computability
量子物理
2007-05-23 v2
摘要
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.
引用
@article{arxiv.quant-ph/0304128,
title = {Transcending the Limits of Turing Computability},
author = {Vadim A. Adamyan and Cristian S. Calude and Boris S. Pavlov},
journal= {arXiv preprint arXiv:quant-ph/0304128},
year = {2007}
}
备注
13 pages, 1 figure