Results 1 
4 of
4
Foliations for solving equations in groups: free, virtually free, and hyperbolic groups
, 2009
"... We give an algorithm for solving equations and inequations with rational constraints in virtually free groups. Our algorithm is based on Rips classification of measured band complexes. Using canonical representatives, we deduce an algorithm for solving equations and inequations in hyperbolic groups ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
We give an algorithm for solving equations and inequations with rational constraints in virtually free groups. Our algorithm is based on Rips classification of measured band complexes. Using canonical representatives, we deduce an algorithm for solving equations and inequations in hyperbolic groups (maybe with torsion). Additionnally, we can deal with quasiisometrically embeddable rational constraints.
Compressed word problems in HNNextensions and amalgamated products
, 811
"... Abstract. It is shown that the compressed word problem for an HNNextension 〈H,t  t −1 at = ϕ(a)(a ∈ A) 〉 with A finite is polynomial time Turingreducible to the compressed word problem for the base group H. An analogous result for amalgamated free products is shown as well. 1 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract. It is shown that the compressed word problem for an HNNextension 〈H,t  t −1 at = ϕ(a)(a ∈ A) 〉 with A finite is polynomial time Turingreducible to the compressed word problem for the base group H. An analogous result for amalgamated free products is shown as well. 1
Bottomup rewriting for words and terms
, 2009
"... For the whole class of linear term rewriting systems, we define bottomup rewriting which is a restriction of the usual notion of rewriting. We show that bottomup rewriting effectively inversepreserves recognizability and analyze the complexity of the underlying construction. The BottomUp class (B ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
For the whole class of linear term rewriting systems, we define bottomup rewriting which is a restriction of the usual notion of rewriting. We show that bottomup rewriting effectively inversepreserves recognizability and analyze the complexity of the underlying construction. The BottomUp class (BU) is, by definition, the set of linear systems for which every derivation can be replaced by a bottomup derivation. Membership to BU turns out to be undecidable, we are thus lead to define more restricted classes: the classes SBU(k), k ∈ N of Strongly BottomUp(k) systems for which we show that membership is decidable. We define the class of SBU(k). We give a polynomial sufficient condition for a system to be in SBU. The class SBU contains (strictly) several classes of systems which were already known to inverse preserve recognizability: the inverse leftbasic semiThue systems (viewed as unary term rewriting systems), the linear growing term rewriting systems, the inverse LinearFinitePathOrdering systems. Strongly BottomUp systems by SBU = S k∈N