Knapsack problems in products of groups

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• 作者：Elizaveta Frenkel^a ; ^{lizzy.frenkel@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Andrey Nikolaev^b ; ^{anikolae@stevens.edu" class="auth_mail" title="E-mail the corresponding author} ; Alexander Ushakov^b ; ^{aushakov@stevens.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：03D15 ; 20F65 ; 20F10 ; 68Q45
• 刊名：Journal of Symbolic Computation
• 出版年：2016
• 出版时间：May-June 2016
• 年：2016
• 卷：74
• 期：Complete
• 页码：96-108
• 全文大小：452 K

文摘

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.