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Partially commutative inverse monoids

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Abstract

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.

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Authors and Affiliations

  1. FMI, Universität Stuttgart, Stuttgart, Germany

    Volker Diekert & Alexander Miller

  2. Institut für Informatik, Universität Leipzig, Leipzig, Germany

    Markus Lohrey

Authors
  1. Volker Diekert
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  2. Markus Lohrey
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  3. Alexander Miller
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Correspondence to Markus Lohrey.

Additional information

Communicated by Benjamin Steinberg.

The work on this paper has been supported by the DFG research project GELO (Graphen mit entscheidbaren Logiken).

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Diekert, V., Lohrey, M. & Miller, A. Partially commutative inverse monoids. Semigroup Forum 77, 196–226 (2008). https://doi.org/10.1007/s00233-008-9060-x

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