Partially commutative inverse monoids

Authors:
Volker Diekert;Markus Lohrey;Alexander Miller
Affiliations:
FMI, Universität Stuttgart, Germany;FMI, Universität Stuttgart, Germany;FMI, Universität Stuttgart, Germany
Venue:
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Year:
2006

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Abstract

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.