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A Note on Nielsen Reduction and Coset Enumeration
 In Proc. ISSAC'98
, 1997
"... Groups can be studied using methods from different fields such as combinatorial group theory or string rewriting. Recently techniques from Grobner basis theory for free monoid rings (noncommutative polynomial rings) respectively free group rings have been added to the set of methods due to the fact ..."
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Cited by 15 (4 self)
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Groups can be studied using methods from different fields such as combinatorial group theory or string rewriting. Recently techniques from Grobner basis theory for free monoid rings (noncommutative polynomial rings) respectively free group rings have been added to the set of methods due to the fact that monoid and group presentations (in terms of string rewriting systems) can be linked to special polynomials called binomials. In the same mood, the aim of this paper is to discuss the relation between Nielsen reduced sets of generators and the ToddCoxeter coset enumeration procedure on the one side and the Grobner basis theory for free group rings on the other. While it is wellknown that there is a strong relationship between Buchberger's algorithm and the KnuthBendix completion procedure, and there are interpretations of the ToddCoxeter coset enumeration procedure using the KnuthBendix procedure for special cases, our aim is to show how a verbatim interpretation of the ToddCoxete...
Partially commutative inverse monoids
 PROCEEDINGS OF THE 31TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS 2006), BRATISLAVE (SLOVAKIA), NUMBER 4162 IN LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... 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)) algo ..."
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Cited by 2 (2 self)
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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 NPcompleteness 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.
Amalgams Of Free Inverse Semigroups
, 1996
"... We study inverse semigroup amalgams of the form S U T where S and T are free inverse semigroups and U is an arbitrary finitely generated inverse subsemigroup of S and T . We make use of recent work of Bennett to show that the word problem is decidable for any such amalgam. This is in contrast to ..."
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We study inverse semigroup amalgams of the form S U T where S and T are free inverse semigroups and U is an arbitrary finitely generated inverse subsemigroup of S and T . We make use of recent work of Bennett to show that the word problem is decidable for any such amalgam. This is in contrast to the general situation for semigroup amalgams, where recent work of Birget, Margolis and Meakin shows that the word problem for a semigroup amalgam S U T is in general undecidable, even if S and T have decidable word problem, U is a free semigroup, and the membership problem for U in S and T is decidable. We also obtain a number of results concerning the structure of such amalgams. We obtain conditions for the Dclasses of such an amalgam to be finite and we show that the amalgam is combinatorial in such a case. For example every onerelator amalgam of this type has finite Dclasses and is combinatorial. We also obtain information concerning when such an amalgam is E unitary: for ...