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Equations Over Free Inverse Monoids with Idempotent Variables

Diekert, Volker ; Martin, Florent ; Sénizergues, Géraud ; Silva, Pedro V.


We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEX-PTIME) whether a system of equations in idempotent variables over a free inverse monoid has a solution. Moreover the problem becomes hard for DEXPTIME, as soon as the quotient group of the free inverse monoid has rank at least two. The upper ...


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