Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds for Combinatorial Algorithms for Boolean Matrix
  Multiplication   In this paper we propose models of combinatorial algorithms for the Boolean
Matrix Multiplication (BMM), and prove lower bounds on computing BMM in these
models. First, we give a relatively relaxed combinatorial model which is an
extension of the model by Angluin (1976), and we prove that the time required
by any algorithm for the BMM is at least $\Omega(n^3 / 2^{O( \sqrt{ \log n
})})$. Subsequently, we propose a more general model capable of simulating the
"Four Russians Algorithm". We prove a lower bound of $\Omega(n^{7/3} /
2^{O(\sqrt{ \log n })})$ for the BMM under this model. We use a special class
of graphs, called $(r,t)$-graphs, originally discovered by Rusza and Szemeredi
(1978), along with randomization, to construct matrices that are hard instances
for our combinatorial models.

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The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: econ