Measuring cones and other thick subsets in free groups

Document Type: Research Paper

Authors

1 Moscow State University

2 Mathematical Institute SB RAS

Abstract

In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they accept‎. ‎We 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 monoids‎. ‎These automata allow us to compute explicitly generating functions‎, ‎$\lambda-$measures and Cesaro measure of thick monoids‎. ‎Also we improve the asymptotic classification of regular subsets in free groups‎.

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