12 citations · 64 across the 32 of their papers we have counts for
4 papers · 1 filter
More Than 1700 Years of Word Equations
Volker Diekert
Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical st…
Solution sets for equations over free groups are EDT0L languages -- ICALP 2015 version
Laura Ciobanu, Volker Diekert, Murray Elder
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 languag…
Equations over free inverse monoids with idempotent variables
Volker Diekert, Florent Martin, Geraud Senizergues +1
We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEXPTIME) whether a system…
Finding All Solutions of Equations in Free Groups and Monoids with Involution
Volker Diekert, Artur Jeż, Wojciech Plandowski
The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as w…