# Publication details

##
Constructive Many-one Reduction from the Halting Problem to Semi-unification

Andrej Dudenhefner

30th EACSL Annual Conference on Computer Science Logic (CSL 2022), Vol. 216 of Leibniz International Proceedings in Informatics (LIPIcs), pp. 18:1--18:19, Schloss Dagstuhl -- Leibniz-Zentrum für Informatik, 2022

The undecidability of semi-unification (unification combined with matching) has been proven by Kfoury, Tiuryn, and Urzyczyn in the 1990s.
The original argument is by Turing reduction from Turing machine immortality (existence of a diverging configuration).

There are several aspects of the existing work which can be improved upon.
First, many-one completeness of semi-unification is not established due to the use of Turing reductions.
Second, existing mechanizations do not cover a comprehensive reduction from Turing machine halting to semi-unification.
Third, reliance on principles such as KÃ¶nig's lemma or the fan theorem does not support constructivity of the arguments.

Improving upon the above aspects, the present work gives a constructive many-one reduction from the Turing machine halting problem to semi-unification.
This establishes many-one completeness of semi-unification.
Computability of the reduction function, constructivity of the argument, and correctness of the argument is witnessed by an axiom-free mechanization in the Coq proof assistant.
The mechanization is incorporated into the existing Coq library of undecidability proofs.
Notably, the mechanization relies on a technique invented by Hooper in the 1960s for Turing machine immortality.

An immediate consequence of the present work is an alternative approach to the constructive many-one equivalence of System F typability and System F type checking, compared to the argument established in the 1990s by Wells.

Download PDF
Show BibTeX

@PROCEEDINGS{Dudenhefner:2022:SemiUnification,
title = {Constructive Many-one Reduction from the Halting Problem to Semi-unification},
author = {Andrej Dudenhefner},
year = {2022},
editor = {Manea, Florin and Simpson, Alex},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
booktitle = {30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {216},
pages = {18:1--18:19},
address = {Dagstuhl, Germany},
howpublished = {https://drops.dagstuhl.de/opus/volltexte/2022/15738},
}

Login to edit

Legal notice, Privacy policy