A fast search algorithm for 〈m,m,m〉 Triple Product Property triples and an application for 5×5 matrix multiplication
نویسندگان
چکیده
منابع مشابه
Search and test algorithms for Triple Product Property triples
In 2003 Cohn and Umans introduced a group-theoretic approach to fast matrix multiplication. This involves finding large subsets of a group G satisfying the Triple Product Property (TPP) as a means to bound the exponent ω of matrix multiplication. We present two new characterizations of the TPP, which are useful for theoretical considerations and for TPP test algorithms. With this we describe al...
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This review paper describes certain elementary methods of group theory for studying the algebraic complexity of matrix multiplication, as measured by the exponent 2 ≤ ω ≤ 3 of matrix multiplication. which is conjectured to be 2. The seed of these methods lies in two ideas of H. Cohn, C. Umans et. al., firstly, that it is possible to " realize " a matrix product via the regular algebra of a (fin...
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15 صفحه اولA Short Note on Disjointness Conditions for Triples of Group Subsets Satisfying the Triple Product Property
(See [2] for a basic de nition.) The TPP property for the triple (S, T, U) is invariant under permutations of the triple, that is, the permuted triples (S,U, T ), (T, S, U), (T,U, S), (U, S, T ), (U, T, S) all satisfy the TPP i (S, T, U) satis es the TPP, ([6], p. 45). We denote by =(G) the set of all TPP triples of G, and by =(G)/Sym3 the set of equivalence classes of =(G) under the equivalenc...
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ژورنال
عنوان ژورنال: Groups Complexity Cryptology
سال: 2015
ISSN: 1867-1144,1869-6104
DOI: 10.1515/gcc-2015-0001