How to Make A Proof of Halting Problem More Convincing: A Pedagogical Remark

Authors

Benjamin W. Robertson, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

12-2017

Comments

Technical Report: UTEP-CS-17-94

Published in International Mathematical Forum, 2018, Vol. 13, No. 1, pp. 9-13.

Abstract

As an example of an algorithmically undecidable problem, most textbooks list the impossibility to check whether a given program halts on given data. A usual proof of this result is based on the assumption that the hypothetical halt-checker works for all programs. To show that a halt-checker is impossible, we design an auxiliary program for which the existence of such a halt-checker leads to a contradiction. However, this auxiliary program is usually very artificial. So, a natural question arises: what if we only require that the halt-checker work for reasonable programs? In this paper, we show that even with such a restriction, halt-checkers are not possible -- and thus, we make a proof of halting problem more convincing for students.