Constructive Many-one Reduction from the Halting Problem to Semi-unification (Extended Version)
Semi-unification is the combination of first-order unification and first-order matching. The undecidability of semi-unification has been proven by Kfoury, Tiuryn, and Urzyczyn in the 1990s by Turing reduction from Turing machine immortality (existence of a diverging configuration). The particular Tu...
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| Published in: | Logical methods in computer science Vol. 19, Issue 4 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V
08.12.2023
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| Subjects: | |
| ISSN: | 1860-5974, 1860-5974 |
| Online Access: | Get full text |
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| Summary: | Semi-unification is the combination of first-order unification and
first-order matching. The undecidability of semi-unification has been proven by
Kfoury, Tiuryn, and Urzyczyn in the 1990s by Turing reduction from Turing
machine immortality (existence of a diverging configuration). The particular
Turing reduction is intricate, uses non-computational principles, and involves
various intermediate models of computation. The present work gives a
constructive many-one reduction from the Turing machine halting problem to
semi-unification. This establishes RE-completeness of semi-unification under
many-one reductions. 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. Arguably, this serves as
comprehensive, precise, and surveyable evidence for the result at hand. The
mechanization is incorporated into the existing, well-maintained Coq library of
undecidability proofs. Notably, a variant of Hooper's argument for the
undecidability of Turing machine immortality is part of the mechanization. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.46298/lmcs-19(4:22)2023 |