A general solution of binary homogeneous equations over free groups

Equations over Torsion-free Groups Summary Klyachko's Methods and the Solution of Equations over Torsion-free Groups

SUMMARY The question we are concerned with here is the following : Let G be a torsion-free group and consider the free product Ghti of G with an innnite cyclic group (generator t). Let w be an element of Ghti?G and hhwii denote the normal closure of w in G hti, then is the natural homomorphism G ! G hti hhwii injective? Klyachko's paper : \Funny property of sphere and equations over groups" Kl]...

Solution Sets for Equations over Free Groups are EDT0L Languages

We show that, given an equation over a finitely generated free group, the set of all solutions in reduced words forms an effectively constructible EDT0L language. Thus, for each equation there is a construction of a Lindenmayer system which generates all solutions in reduced words. In particular, the set of all solutions in reduced words is an indexed language in the sense of Aho. The language ...

On General Solution of Equations in a Free Semigroup

Solution sets for equations over free groups are EDT0L languages -- ICALP 2015 version

We show that, given a word equation over a finitely generated free group, the set of all solutions in reduced words forms an EDT0L language. In particular, it is an indexed language in the sense of Aho. The question of whether a description of solution sets in reduced words as an indexed language is possible has been been open for some years [9, 10], apparently without much hope that a positive...

On the coordinate groups of irreducible systems of equations in two variables over free groups

We describe the fully residually F groups; or limit groups relative to F ; that arise from systems of equations in two variables over a free group F that have coefficients in F .