4 papers
Solutions of Word Equations over Partially Commutative Structures
Volker Diekert, Artur Jeż, Manfred Kufleitner +1
Let be a free partially commutative monoid with involution and its quotient group (for example, a right-angled Artin or Coxeter group). We show that for any syste…
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…
Quadratic word equations with regular constraints and the exponent of periodicity
Volker Diekert, Silas Natterer, Alexander Thumm
In this article, we study word equations in free semigroups and the conjecture that the existence of infinitely many solutions entails the existence of solutions with arbitrarily l…
Decidability of membership problems for flat rational subsets of and singular matrices
Volker Diekert, Igor Potapov, Pavel Semukhin
We consider membership problems for rational subsets of the semigroup of matrices over . For a semigroup , the rational subsets are def…