The Recursion Theorem from a Different Angle

Abstract

This paper is about computability. I claim the likely existence of a program DoesHalt(Program, Input) such that DoesHalt( HaltsOnItself, AntiSelf ) halts with resounding 'NO'. HaltsOnItself( Program ) is simply DoesHalt( Program, Program ). AntiSelf() is a self-referential self-contradictory program that loops when HaltsOnItself() returns 'YES' and halts when HaltsOnItself() returns 'NO'.

arXiv commentThis paper has been superseded by "Getting around the Halting Problem" https://arxiv.org/abs/1706.03392