Groups Complexity Cryptology
Managing Editor: Rosenberger, Gerhard / Shpilrain, Vladimir
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Search and witness problems in group theory
1Department of Mathematics, The City College of New York, New York, NY 10031, USA. E-mail: (email)
Citation Information: Groups – Complexity – Cryptology. Volume 2, Issue 2, Pages 231–246, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: 10.1515/gcc.2010.015, November 2010
- Published Online:
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.
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