On the complexity of matrix product
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Parsing expression grammars: a recognition-based syntactic foundation
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Beyond the Alder-Strassen bound
Theoretical Computer Science - Automata, languages and programming
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We prove lower bounds on the number of product gates in bilinear and quadratic circuits that compute the product of two n 脳 n matrices over finite fields. In particular we obtain the following results:1. We show that the number of product gates in any bilinear (or quadratic) circuit that computes the product of two n 脳 n matrices over GF(2) is at least 3n^2- o(n^2 ).2. We show that the number of product gates in any bilinear circuit that computes the product of two n 脳 n matrices over GF(p) is at least (2.5 + \frac{{1.5}}{{p^3- 1}})n^2- o(n^2).These results improve the former results of [3, 1] who proved lower bounds of 2.5n^2- o(n^2).