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Search and witness problems in group theory
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Vladimir Shpilrain
Published/Copyright:
November 15, 2010
Abstract
Decision problems are problems of the following nature: given a property 
and an object 
, find out whether or not the object has the property . On the other hand, witness problems are: given a property and an object with the property , find a proof of the fact that indeed has the property .
On the third hand(?!), search problems are of the following nature: given a property and an object with the property , find something “material” establishing the property ; for example, given two conjugate elements of a group, find a conjugator. In this survey our focus is on various search problems in group theory, including the word search problem, the subgroup membership search problem, the conjugacy search problem, and others.
Received: 2010-08-01
Published Online: 2010-11-15
Published in Print: 2010-December
© de Gruyter 2010
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- On finite Thurston-type orderings of braid groups
- Subgroup conjugacy problem for Garside subgroups of Garside groups
- The Latin squares and the secret sharing schemes
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Articles in the same Issue
- On asymptotic densities and generic properties in finitely generated groups
- On finite Thurston-type orderings of braid groups
- Subgroup conjugacy problem for Garside subgroups of Garside groups
- The Latin squares and the secret sharing schemes
- A note on the homology of hyperbolic groups
- Cutting up graphs revisited – a short proof of Stallings' structure theorem
- Some geodesic problems in groups
- Search and witness problems in group theory
- Algebraic attacks using SAT-solvers
