2014/12/11 by Volker Diekert, Florent Martin, Diekert, Volker +5
Computer Science · #03D40 #20F70 #20M18 #F.2 #F.2.2 #F.4 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1412.4737
openalex publication_date 2014/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEXPTIME) whether a system of equations in idempotent variables over a free inverse monoid has a solution. The result is proved by a direct reduction to solve language equations with one-sided concatenation and a known complexity result by Baader and Narendran: Unification of concept terms in description logics, 2001. We also show that the problem becomes DEXPTIME hard , as soon as the quotient group of the free inverse monoid has rank at least two. Decidability for systems of typed equations over a free inverse monoid with one irreducible variable and at least one unbalanced equation is proved with the 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 decidability has been previously known.