Partially Commutative Inverse Monoids

  • Volker Diekert
  • Markus Lohrey
  • Alexander Miller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)


Free partially commutative inverse monoids are investigated. Analogously to free partially commutative monoids (trace monoids), free partially commutative inverse monoid are the quotients of free inverse monoids modulo a partially defined commutation relation on the generators. An O(n log(n)) algorithm on a RAM for the word problem is presented, and NP-completeness of 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. For these monoids, the word problem is decidable if and only if the complement of the commutation relation is transitive.


Word Problem Inverse Semigroup Cayley Graph Dependence Graph Dependence Relation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Volker Diekert
    • 1
  • Markus Lohrey
    • 1
  • Alexander Miller
    • 1
  1. 1.FMIUniversität StuttgartGermany

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