B. Reinert, T. Mora, and K. Madlener. A note on nielsen reduction and coset enumeration. In O. Gloor, editor, Proc. ISSAC'98, pages 171--178. ACM, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

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B. Reinert, T. Mora, and K. Madlener. A note on nielsen reduction and coset enumeration. In O. Gloor, editor, Proc. ISSAC'98, pages 171--178. ACM, 1998.

....not involve in fact arithmetical operations; its complexity is rather characterized by L(u) reduction steps. This kind of ideals is strongly related to monoid presentations (cf. MR] for a recent study regarding this relation) We also remark that in the same mood FGLM algorithm has been used in [RMM] in their interpretation of Todd Coxeter Algorithm in terms of Grobner techniques. 2. FGLM algorithm for free associative algebras In this section we present our generalization, for free associative algebras, of the FGLM algorithm. The procedure we are presenting is based on a sort of black box ....

Reinert B., Madlener K., Mora T. (1998). "A Note on Nielsen Reduction and Coset Enumeration." In: Proc. ISSAC 98, pp. 171-178.

....[4] But is still far from the best results achieved by optimizing the enumeration by hand which only needs 53 cosets before the collaps occurs. Examining more Knuth Bendix or other orderings might improve the performance of our program further. In this paper we show how the procedure presented in [11] for theoretical reasons to show how rewriting methods and Todd Coxeter are related, can be improved when having real computation in mind. In order to do so, we introduce so called frameworks which can be compared to the strategies Felsch and HLT for the original Todd Coxeter enumeration ....

....reader is familiar with the methods available for coset enumeration. Descriptions of these methods can be found in [16, 1, 8, 3, 15] The description of the procedure simulating the Todd Coxeter procedure using pre x Gr obner bases and a comparison with Knuth Bendix completion can be found in 2 [11]. The Paper is organized as follows. In Section 2 we shortly recall the most important concept from coset enumeration and of the simulating procedure. As this procedure is only appropriate for small examples, we propose two frameworks which are presented in Section 3. They use strategies which are ....

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B. Reinert, T. Mora, and K. Madlener. A note on Nielsen reduction and coset enumeration. In Proc. ISSAC'98, 1998.

....problem for groups and the ideal membership problem for free group rings; ffl between the submonoid problem and the subalgebra problem for monoid rings; ffl and between the subgroup problem and the one sided ideal membership problem for group rings. Another link to group theory is provided in [20]: the well known procedure of Todd and Coxeter for enumerating cosets of a subgroup can be rephrased using prefix Grobner bases (in fact the implementation used to compute the examples there was done in Mrc V 1.0) Here we want to present an implementation of the Grobner basis method using ....

.... and systematically enumerates all cosets of a finitely generated subgroup in a given finitely presented group [23] Nielsen reduced sets allow the computation of Schreier coset representatives hence enabling syntactical solutions to the subgroup problem in finitely generated free groups [18] In [20] Procedure 16 (see page 16) for simulating a combination of both procedures using prefix Grobner bases is developed. It makes use extended todd coxeter simulation Given: FR = fr Gamma 1 j r 2 Rg, a set of binomials representing the relators. FU = fu Gamma 1 j u 2 Ug, a set of binomials ....

B. Reinert, T. Mora, and K. Madlener. A note on Nielsen reduction and coset enumeration. In Proc. ISSAC'98, 1998.

....here again V is the polynomial ring and the functionals are the coe cients in a canonical form of a polynomial by a Gr obner basis. 11] presents the complete theory in the polynomial ring case. M oller Algorithm has been recently generalized in the non commutative polynomial ring setting ([14]) as a tool to interpret Todd Coxeter Algorithm via Gr obner technology, and to the two sided ideal case ( 2] However, hints to M oller Algorithm in non commutative polynomial rings are alrealdy present in [9] which is even older than [6] M oller Algorithm can be informally described as ....

Reinert B., Madlener K., Mora T. A Note on Nielsen Reduction and Coset Enumeration. Proc. ISSAC 98, Rostock (1998),171-178.

....prefix string rewriting methods have been compared to Tc. We recall and compare two of them briefly, one by Kuhn and Madlener [4] and one by Sims [15] A new approach using prefix string rewriting in free groups is derived from the algebraic method presented by Reinert, Mora and Madlener in [14] which directly emulates Tc. It is extended to free monoids and an algebraic characterization for the cosets enumerated in this setting is provided. Keywords. coset enumeration, subgroup problem, prefix string rewriting, Grobner bases in monoid and group rings. 1 Introduction A group G is ....

....diverges while the index is finite, additional knowledge has to be used to determine that the completion process can be stopped (see Section 3. 10 in [15] for more details) We overcome this problem by translating the algebraic characterization of Tc as presented by Reinert, Mora and Madlener in [14] into a prefix string rewriting procedure which can be generalized to the case of monoids. The paper is organized as follows: First we give short introductions to string rewriting theory, the subgroup problem and the Todd Coxeter coset enumeration method. Then in Section 5 we outline the approach ....

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B. Reinert, T. Mora, and K. Madlener. A note on nielsen reduction and coset enumeration. In O. Gloor, editor, Proc. ISSAC'98, pages 171--178. ACM, 1998.

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B. Reinert, K. Madlener, and T. Mora. A note on nielsen reduction and coset enumeration. February 1998.

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