English

A Hypercomputation in Brouwer's Constructivism

Logic in Computer Science 2015-11-17 v2 Formal Languages and Automata Theory

Abstract

In contrast to other constructivist schools, for Brouwer, the notion of "constructive object" is not restricted to be presented as `words' in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished objects are legitimate constructive objects. In this way, Brouwer's constructivism goes beyond Turing computability. Further, in 1999, the term hypercomputation was introduced by J. Copeland. Hypercomputation refers to models of computation which go beyond Church-Turing thesis. In this paper, we propose a hypercomputation called persistently evolutionary Turing machines based on Brouwer's notion of being constructive.

Keywords

Cite

@article{arxiv.1408.2930,
  title  = {A Hypercomputation in Brouwer's Constructivism},
  author = {Rasoul Ramezanian},
  journal= {arXiv preprint arXiv:1408.2930},
  year   = {2015}
}

Comments

This paper has been withdrawn by the author due to crucial errors in theorems 4.6 and 5.2 and definition 4.2

R2 v1 2026-06-22T05:27:27.646Z