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Mathematical Structures in Computer Science Mathematical Structures in Computer Science

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Extensions of unification modulo ACUI

Published online by Cambridge University Press:  11 November 2019

Franz Baader ,
Pavlos Marantidis Open the ORCID record for Pavlos Marantidis[Opens in a new window] ,
Antoine Mottet  and
Alexander Okhotin
Franz Baader
Affiliation:
Theoretical Computer Science, Technische Universität Dresden, Germany
Pavlos Marantidis*
Affiliation:
Theoretical Computer Science, Technische Universität Dresden, Germany
Antoine Mottet
Affiliation:
Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Alexander Okhotin
Affiliation:
St. Petersburg State University, St. Petersburg, Russia
*
*Corresponding author. Email: pavlos.marantidis@tu-dresden.de
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Abstract

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The theory ACUI of an associative, commutative, and idempotent binary function symbol + with unit 0 was one of the first equational theories for which the complexity of testing solvability of unification problems was investigated in detail. In this paper, we investigate two extensions of ACUI. On one hand, we consider approximate ACUI-unification, where we use appropriate measures to express how close a substitution is to being a unifier. On the other hand, we extend ACUI-unification to ACUIG-unification, that is, unification in equational theories that are obtained from ACUI by adding a finite set G of ground identities. Finally, we combine the two extensions, that is, consider approximate ACUI-unification. For all cases we are able to determine the exact worst-case complexity of the unification problem.

Keywords

Unification theoryACUIapproximate unificationground identities
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Special Issue 6: Special Issue: Unification , June 2020 , pp. 597 - 626
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Cambridge University Press 2019

Footnotes

†

Supported by DFG Graduiertenkolleg 1763 (QuantLA).

‡

Partially supported by DFG Graduiertenkolleg 1763 (QuantLA).

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