| Title | : | Average case complexity of the Uniform Membership Problem for subgroups of free groups |
| Speaker | : | Pascal Weil (CNRS researcher) |
| Details | : | Fri, 21 Feb, 2025 11:00 AM @ SSB 334 |
| Abstract: | : | The Uniform Membership Problem for subgroups of a fixed finitely generated group G is the following: given a (k+1)-tuple (g, h_1, ..., h_k) of elements of G (given as words on a set of generators of G), decide whether g sits in the subgroup of G generated by the h_i.
We study the average case complexity of this problem for subgroups of free groups, and we show that it is orders of magnitude smaller than the worst case complexity of the best known algorithms. This applies to subgroups given by a fixed number of generators as well as to subgroups given by an exponential number of generators. The main idea behind this result is to exploit a generic property of tuples of words, called the central tree property.
An application is given to the average case complexity of the Relative Primitivity Problem, using Shpilrain’s recent algorithm to decide primitivity, whose average case complexity is a constant depending only on the rank of the ambient free group.
Speaker Bio : Pascal Weil is the deputy director of the Indo-French CNRS lab ReLaX. He is also a CNRS researcher (DR) at LIPN (Laboratoire d'Informatique de Paris Nord), in the CALIN team. His research interests include automata theory, logic, models of distributed computation, asymptotic theory of infinite groups among many others. |
