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CORR
2002
Springer

Average-case complexity and decision problems in group theory

8 years 10 months ago
Average-case complexity and decision problems in group theory
Abstract. We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on "generic-case complexity" we show that if a finitely generated group G has the word problem solvable in subexponential time and has a subgroup of finite index which possesses a non-elementary word-hyperbolic quotient group, then the average-case complexity of the word problem for G is linear time, uniformly with respect to the collection of all length-invariant measures on G. For example, the result applies to all braid groups Bn.
Ilya Kapovich, Alexei G. Myasnikov, Paul Schupp, V
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2002
Where CORR
Authors Ilya Kapovich, Alexei G. Myasnikov, Paul Schupp, Vladimir Shpilrain
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