10 research outputs found
Double cosets in free groups
In this paper we study double cosets of finite rank free groups. We focus our
attention on cancellation types in double cosets and their formal language
properties.Comment: Minor change
Knapsack problems in products of groups
The classic knapsack and related problems have natural generalizations to
arbitrary (non-commutative) groups, collectively called knapsack-type problems
in groups. We study the effect of free and direct products on their time
complexity. We show that free products in certain sense preserve time
complexity of knapsack-type problems, while direct products may amplify it. Our
methods allow to obtain complexity results for rational subset membership
problem in amalgamated free products over finite subgroups.Comment: 15 pages, 5 figures. Updated to include more general results, mostly
in Section
Measuring cones and other thick subsets in free groups
In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they acceptâ. âWe show how one can decompose an arbitrary regular subset of a finite rank free group into disjoint union of sets accepted by special automata or special monoidsâ. âThese automata allow us to compute explicitly generating functionsâ, âmeasures and Cesaro measure of thick monoidsâ. âAlso we improve the asymptotic classification of regular subsets in free groupsâ