We study equations in groups G with unique m-th roots for each positive integer m. A word equation in two letters is an expression of the form w(X,A) = B, where w is a finite word in the alphabet {X,A}. We think of A,B ∈ G as fixed coefficients, and X ∈ G as the unknown. Certain word equations, such as XAXAX = B, have solutions in terms of radicals: X = A(ABA)A while others such as XAX = B do n...

 Suppose $f$ is a map from a non-empty finite set $X$ to a finite group $G$. Define the map $zeta^f_G: Glongrightarrow mathbb{N}cup {0}$ by $gmapsto |f^{-1}(g)|$. In this article, we show that for a suitable choice of $f$, the map $zeta^f_G$ is a character. We use our results to show that the solution function for the word equation $w(t_1,t_2,dots,t_n)=g$ ($gin G$) is a character, where $w(t_1,...

The paper focuses on the automatic generating of witnesses for word equation satisfiability problem by means specializing an interpreter which tests whether a composition variable substitutions given system produces its solution. We specialize such w.r.t. system, while are unknown. show that several variants interpreters, when specialized using basic unfold/fold specialization methods, able to ...

Word equations are a fundamental part of combinatorics on words, see e.g. [20] or [2] for a general reference on these subjects. One of the basic results in the theory of word equations is that a nontrivial equation causes a defect effect. In other words, if n words satisfy a nontrivial relation, then they can be represented as products of n− 1 words. Not much is known about the additional rest...

i DECLARATION I, the undersigned, hereby declare that the work contained in this thesis is my own original work and that I have not previously in its entirety or in part submitted it at any university for a degree. Signature Date ii ABSTRACT This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework is established in the initial...