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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board Member: Blackburn, Simon R. / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Schäge, Sven / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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Search and witness problems in group theory

Vladimir Shpilrain
Published Online: 2010-11-15 | DOI: https://doi.org/10.1515/gcc.2010.015


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.

Keywords.: Algorithmic problems; search problems; stratification

About the article

Received: 2010-08-01

Published Online: 2010-11-15

Published in Print: 2010-12-01

Citation Information: Groups – Complexity – Cryptology, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc.2010.015. Export Citation

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