5 papers · 1 filter
Twisted Equations and Palindrome Length
Volker Diekert, Anna E. Frid, Silas Natterer +1
Twisted equations in free groups are equations in which a finite group of symmetries acts on the free group by automorphisms and anti-automorphisms, such as inversion and reversal;…
Word Length and Diameter in Permutation Groups
Markus Lohrey, Alexander Thumm
The input for the binary diameter problem consists of explicitly represented permutations generating a finite group and a binary-encoded nonnegative integer . The question i…
Quadratic Equations in Graph Products of Groups and the Exponent of Periodicity
Volker Diekert, Silas Natterer, Alexander Thumm
In 1977, Makanin established the decidability of equations in free monoids. A key ingredient in his proof is the exponent of periodicity: for a word , it is the largest exponent…
Finite groups with geodetic Cayley graphs
Murray Elder, Adam Piggott, Florian Stober +2
A connected undirected graph is called \emph{geodetic} if for every pair of vertices there is a unique shortest path connecting them. It has been conjectured that for finite groups…
Streaming algorithms for groups and semigroups
Markus Lohrey, Lukas Lück, Alexander Thumm +1
We investigate deterministic and randomized streaming algorithms for word problems in finitely generated groups and semigroups. For this we introduce the notion of a distinguisher:…