Average-case complexity and decision problems in group theory
نویسندگان
چکیده
منابع مشابه
Average-case complexity and decision problems in group theory
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 word problem solvable in subexponential time and has a subgroup of finite index which possesses a non-elementary word-hyperbolic quotient group, then t...
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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 solv-able in subexponential time and has a subgroup of finite index which possesses a non-elementary word-hyperbolic quotient group,...
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Informally, Average case Complexity theory considers the average complexity with respect to a probability distribution over the set of inputs, instead of the complexity on the worst case input, as a criterion for the hardness of a problem. With regard to this theory, we explore the notion of a natural distribution. In particular, we consider different bounds on the minentropy of such distributi...
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We give a precise definition of “generic-case complexity” and show that for a very large class of finitely generated groups the classical decision problems of group theory the word, conjugacy and membership problems all have linear-time generic-case complexity. We prove such theorems by using the theory of random walks on regular graphs.
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We give a precise definition of “generic-case complexity” and show that for a very large class of finitely generated groups the classical decision problems of group theory the word, conjugacy and membership problems all have linear-time generic-case complexity. We prove such theorems by using the theory of random walks on regular graphs.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2005
ISSN: 0001-8708
DOI: 10.1016/j.aim.2003.02.001