EasyChair Publications
Paper Information
Paper:Michael Fiske
Turing Incomputable Computation
Title:Turing Incomputable Computation
Authors:Michael Fiske
Keyphrases:active element, boolean function, firing pattern, hypercomputation, incomputable, level set, quantum random, time, turing machine
Abstract:A new computing model, called the active element machine (AEM), is presented that demonstrates Turing incomputable computation using quantum random input. The AEM deterministically executes a universal Turing machine (UTM) program η with random active element firing patterns. These firing patterns are Turing incomputable when the AEM executes a UTM having an unbounded number of computable steps. For an unbounded number of computable steps, if zero information is revealed to an adversary about the AEM’s representation of the UTM’s state and tape and the quantum random bits that help determine η’s computation and zero information is revealed about the dynamic connections between the active elements, then there does not exist a “reverse engineer” Turing machine that can map the random firing patterns back to the sequence of UTM instructions. This casts a new light on Turing’s notion of a computational procedure. In practical terms, these methods present an opportunity to build a new class of computing machines where the program’s computational steps are hidden. This non-Turing computing behavior may be useful in cybersecurity and in other areas such as machine learning where multiple, dynamic interpretations of firing patterns may be applicable.
Volume:Andrei Voronkov (editor). Turing-100. The Alan Turing Centenary
Series:EPiC Series in Computing
Volume number:10
Editors:Andrei Voronkov
Page views:123
BibTeX entry:
  author    = {Michael Stephen Fiske},
  title     = {Turing Incomputable Computation},
  booktitle = {Turing-100. The Alan Turing Centenary},
  editor    = {Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {10},
  pages     = {66-91},
  year      = {2012},
  publisher = {EasyChair},
  bibsource = {EasyChair, http://www.easychair.org},
  issn      = {2398-7340}}