The Nielsen reduction and P-complete problems in free groups
Theoretical Computer Science
Journal of Computer and System Sciences
A method for enumerating cosets of a group presented by a canonical system
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
A specialized completion procedure for monadic string-rewriting systems presenting groups
Proceedings of the 18th international colloquium on Automata, languages and programming
String-rewriting systems
Computing presentations for subgroups of context-free groups
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
An Effective Version of Stallings' Theorem in the Case of Context-Free Groups
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
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Canonical presentations of groups are of interest, since they provide structurally simple algorithms for computing normal forms. A class of groups that has received much attention is the class of context-free groups. This class of groups can be characterized algebraically as well as through some language-theoretical properties as well as through certain combinatorial properties of presentations. Here we use the fact that a finitely generated group is context-free if and only if it admits a finite canonical presentation of a certain form that we call a virtually free presentation. Since finitely generated subgroups of context-free groups are again context-free, they admit presentations of the same form. We present a polynomial-time algorithm that, given a finite virtually free presentation of a context-free group G and a finite subset U of G as input, computes a virtually free presentation for the subgroup U of G that is generated by U.