English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce the notion of idempotent variables for studying equations ininverse monoids.  It is proved that it is decidable in singly exponential time (DEXPTIME)whether a system of equations in idempotent variables over a free inversemonoid has a solution. The result is proved by a direct reduction to solvelanguage equations with one-sided concatenation and a known complexity resultby Baader and Narendran: Unification of concept terms in description logics,2001. We also show that the problem becomes DEXPTIME hard , as soon as thequotient group of the free inverse monoid has rank at least two.  Decidability for systems of typed equations over a free inverse monoid withone irreducible variable and at least one unbalanced equation is proved withthe same complexity for the upper bound.  Our results improve known complexity bounds by Deis, Meakin, and Senizergues:Equations in free inverse monoids, 2007.  Our results also apply to larger families of equations where no decidabilityhas been previously known.

Equations over free inverse monoids with idempotent variables