The Nielsen reduction and P-complete problems in free groups
Theoretical Computer Science
Thue systems as rewriting systems
Proc. of the first international conference on Rewriting techniques and applications
Groups presented by certain classes of finite length-reducing string rewriting systems
on Rewriting techniques and applications
On deciding the confluence of a finite string-rewriting system on a given congruence class
Journal of Computer and System Sciences
Using rewriting techniques to solve the generalized word problem in polycyclic groups
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Computations with Rational Subsets of Confluent Groups
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Computing presentations for subgroups of context-free groups
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Computing Gröbner bases in monoid and group rings
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Checking Simple Properties of Transition Systems Defined by Thue Specifications
Journal of Automated Reasoning
On the Connections between Rewriting and Formal Language Theory
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
A structural approach to reversible computation
Theoretical Computer Science
Finite derivation type for Rees matrix semigroups
Theoretical Computer Science
Representation of a class of nondeterministic semiautomata by canonical words
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
| Hi-index | 0.00 |
The application of rewriting techniques to enumerate cosets of subgroups in groups is investigated. Given a class of groups G having canonical string rewriting presentations we consider the GWP for this class which is defined by GWP(w,U) iff w ∈ for w ∈ G, finite U⊆G, G ∈ G where is the subgroup of G generated by U. We show how to associate to U two rewriting relations @@@@U and @@@@U on strings such that w ∈ iff w @@@@U &lgr; iff w @@@@U &lgr; (&lgr; the empty word), both representing the left congruence generated by . We derive general critical pair criteria for confluence and &lgr;-confluence for these relations. Using these criteria completion procedures can be constructed which enumerate cosets like the Todd-Coxeter algorithm without explicit definition of all cosets. The procedures are shown to be terminating if the index of the subgroup is finite or for groups with finite canonical monadic group presentations. If the completion procedure terminates it returns a prefix rewriting system which is confluent on &Sgr;*, thus deciding the GWP and the index problem for this class of groups. The normal forms of the rewriting relations form a minimal Schreier-representative system of in G.