10 research outputs found

    Double cosets in free groups

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    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

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    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

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    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, ‎lambdalambda-measures and Cesaro measure of thick monoids‎. ‎Also we improve the asymptotic classification of regular subsets in free groups‎


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