Efficient testing of groups

We construct an efficient probabilistic algorithm that, given a finite set with a binary operation, tests if it is an abelian group. The distance used is an analogue of the edit distance for strings. The query complexity of the tester is polylogarithmic in the size of the set. Previous testers used Hamming type distances and had superlinear query complexity. A building block for our construction is a constant query complexity homomorphism tester for functions mapping an given finite group into an arbitrary set equipped with a binary operation. Categories and Subject Descriptors F.2 [Analysis of algorithms and problem complexity]: Miscellaneous General Terms Algorithms, Theory Keywords Group multiplication testing, edit distance, probabilistic computation, quantum computation

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Katalin Friedl, Gábor Ivanyos, Miklos Santha
• Keywords: Algorithms, Efficient Probabilistic Algorithm, Miscellaneous General Terms, Query Complexity, STOC 2005