License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2020.9
URN: urn:nbn:de:0030-drops-123311
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Dudenhefner, Andrej

Undecidability of Semi-Unification on a Napkin

LIPIcs-FSCD-2020-9.pdf (0.5 MB)


Semi-unification (unification combined with matching) has been proven undecidable by Kfoury, Tiuryn, and Urzyczyn in the 1990s. The original argument reduces Turing machine immortality via Turing machine boundedness to semi-unification. The latter part is technically most challenging, involving several intermediate models of computation.
This work presents a novel, simpler reduction from Turing machine boundedness to semi-unification. In contrast to the original argument, we directly translate boundedness to solutions of semi-unification and vice versa. In addition, the reduction is mechanized in the Coq proof assistant, relying on a mechanization-friendly stack machine model that corresponds to space-bounded Turing machines. Taking advantage of the simpler proof, the mechanization is comparatively short and fully constructive.

BibTeX - Entry

  author =	{Andrej Dudenhefner},
  title =	{{Undecidability of Semi-Unification on a Napkin}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Zena M. Ariola},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-123311},
  doi =		{10.4230/LIPIcs.FSCD.2020.9},
  annote =	{Keywords: undecidability, semi-unification, mechanization}

Keywords: undecidability, semi-unification, mechanization
Collection: 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)
Issue Date: 2020
Date of publication: 28.06.2020
Supplementary Material:

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