, 57 M 05 Average - Case Complexity and Decision Problems in Group Theory
نویسندگان
چکیده
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, 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.
منابع مشابه
Quotient tests and random walks in computational group theory
For many decision problems on a finitely presented group G, we can quickly weed out negative solutions by using much quicker algorithms on an appropriately chosen quotient group G/K of G. However, the behavior of such “quotient tests” can be sometimes paradoxical. In this paper, we analyze a few simple case studies of quotient tests for the classical identity, word, conjugacy problems in groups...
متن کاملMultiple attribute group decision making with linguistic variables and complete unknown weight information
Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are a very useful means to depict the linguistic information in the process of decision making. In this article, we investigate the group decision making problems in which all the linguistic information provided by the decision makers is expressed as interval type-2 fuzzy decision matrices where each of ...
متن کاملAverage-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...
متن کاملSoft Computing-based New Interval-valued Pythagorean Triangular Fuzzy Multi-criteria Group Assessment Method without Aggregation: Application to a Transport Projects Appraisal
In this paper, an interval-valued Pythagorean triangular fuzzy number (IVPTFN) as a useful tool to handle decision-making problems with vague quantities is defined. Then, their operational laws are developed. By introducing a novel method of making a decision on the concept of possibility theory, a multi-attribute group decision-making (MAGDM) problem is considered, in which the attribute value...
متن کاملGeneric-case Complexity, Decision Problems in Group Theory and Random Walks
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
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002