Neural hypercomputation: A decisional approach
Ashish Sharma, Arvind Kumar Upadhyay · 2016
Deciding the undecidable is the aim of hypercomputation community. Recently there are various claims of hypercomputation and this work examines two of the most celebrated of them in detail. Although Turing machines are believed to be the ultimate model of computation, but the claims of hypercomputation are challenging this notion with great confidence. There are various hypercomputation models based on various theories. Hypercomputation models based on neural networks have developed in recent years, claiming to go beyond the limits set by the Church-Turing thesis. The Church-Turing thesis is the assertion that no machine can compute more than a Turing machine. In this work we will prove that the models considered are not computing the uncomputable and hence, not breaking the Turing barrier. In essence the models cross the Turing limit if and only if they are supplemented with a hypercomputer in advance otherwise they are equivalent to the Turing machine model. The arguments presented in this paper are of prime importance as they are directly applicable to judge other claims of hypercomputation too.