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The Complexity of Knapsack Problems in Wreath Products

2020
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International Colloquium on Automata, Languages and Programming
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We prove new complexity results for computational problems in certain wreath products of groups and (as an application) for free solvable groups. For a finitely generated group we study the so-called power word problem (does a given expression u₁^{k₁} ... u_d^{k_d}, where u₁, ..., u_d are words over the group generators and k₁, ..., k_d are binary encoded integers, evaluate to the group identity?) and knapsack problem (does a given equation u₁^{x₁} ... u_d^{x_d} = v, where u₁, ..., u_d,v are

doi:10.4230/lipics.icalp.2020.126
dblp:conf/icalp/FigeliusGLZ20
fatcat:ptqydcxlknaavoiyhgm42dofci