Semigroup Forum

, Volume 77, Issue 2, pp 196–226 | Cite as

Partially commutative inverse monoids

Research article


Free partially commutative inverse monoids are investigated. As in the case of free partially commutative monoids or groups (trace monoids or graph groups), free partially commutative inverse monoids are defined as quotients of free inverse monoids modulo a partially defined commutation relation on the generators. A quasi linear time algorithm for the word problem is presented. More precisely, we give an \(\mathcal {O}(n\log(n))\) algorithm for a RAM. \(\mathsf {NP}\) -completeness of the submonoid membership problem (also known as the generalized word problem) and the membership problem for rational sets is shown. Moreover, free partially commutative inverse monoids modulo a finite idempotent presentation are studied. It turns out that the word problem is decidable if and only if the complement of the partial commutation relation is transitive.


Inverse monoids Partially commutative monoids Word problems Rational sets 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Volker Diekert
    • 1
  • Markus Lohrey
    • 2
  • Alexander Miller
    • 1
  1. 1.FMIUniversität StuttgartStuttgartGermany
  2. 2.Institut für InformatikUniversität LeipzigLeipzigGermany

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