Published online by Cambridge University Press: 11 November 2019
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.
Supported by DFG Graduiertenkolleg 1763 (QuantLA).
Partially supported by DFG Graduiertenkolleg 1763 (QuantLA).
Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.
* Views captured on Cambridge Core between 11th November 2019 - 24th February 2021. This data will be updated every 24 hours.