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CFG Parsing and Boolean Matrix Multiplication
"... Abstract. In this work the relation between Boolean Matrix Multiplication (BMM) and Context Free Grammar (CFG) parsing is shown. The first described approach, which is due to Valiant (1975), shows how CFG parsing can be reduced to Boolean Matrix Multiplication. Afterwards the reverse direction, i.e ..."
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Abstract. In this work the relation between Boolean Matrix Multiplication (BMM) and Context Free Grammar (CFG) parsing is shown. The first described approach, which is due to Valiant (1975), shows how CFG parsing can be reduced to Boolean Matrix Multiplication. Afterwards the reverse direction, i
A Note on Boolean Matrix Multiplication
, 1995
"... A classical topic in computer science is matrix multiplication and Boolean Matrix Multiplication in particular. Most papers studying these problems present worst case algorithms with running times O(n 2+ff ). For smaller ff these algorithms are rather complex and difficult to understand. As for s ..."
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A classical topic in computer science is matrix multiplication and Boolean Matrix Multiplication in particular. Most papers studying these problems present worst case algorithms with running times O(n 2+ff ). For smaller ff these algorithms are rather complex and difficult to understand
An Improved Combinatorial Algorithm for Boolean Matrix Multiplication
, 2015
"... We present a new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in Ô(n3 / log4 n) time, where the O ̂ notation suppresses poly(loglog) factors. This improves the previous best combinatorial algorithm by Chan [4] that runs in Ô(n3 / log3 n) time. Our algor ..."
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We present a new combinatorial algorithm for triangle finding and Boolean matrix multiplication that runs in Ô(n3 / log4 n) time, where the O ̂ notation suppresses poly(loglog) factors. This improves the previous best combinatorial algorithm by Chan [4] that runs in Ô(n3 / log3 n) time. Our
TreeAdjoining Grammar Parsing and Boolean Matrix Multiplication
, 1994
"... this paper we restate the TAG parsing problem as a search problem and relate it to the wellknown computational problem of Boolean matrix multiplication. This is done in such a way that time upper bounds for TAG parsing can be transferred to time upper bounds for the latter problem. More precisely, ..."
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Cited by 21 (2 self)
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this paper we restate the TAG parsing problem as a search problem and relate it to the wellknown computational problem of Boolean matrix multiplication. This is done in such a way that time upper bounds for TAG parsing can be transferred to time upper bounds for the latter problem. More precisely
A TimeSpace Tradeoff for Boolean Matrix Multiplication
"... A timespace tradeoff is established in the branching program model for the problem of computing the product of two n x n matrices over the semiring ((0, l}, V, A). It is a.ssumed that ea.ch element of each nxn input matrix is chosen independently to be 1 with probability nll2 and to be 0 with prob ..."
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Cited by 12 (0 self)
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A timespace tradeoff is established in the branching program model for the problem of computing the product of two n x n matrices over the semiring ((0, l}, V, A). It is a.ssumed that ea.ch element of each nxn input matrix is chosen independently to be 1 with probability nll2 and to be 0
Fast ContextFree Grammar Parsing Requires Fast Boolean Matrix Multiplication
, 2002
"... In 1975, Valiant showed that Boolean matrix multiplication can be used for parsing contextfree grammars (CFGs), yielding the asympotically fastest (although not practical) CFG parsing algorithm known. We prove a dual result: any CFG parser with time complexity $O(g n^{3  \epsilson})$, where $g$ is ..."
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Cited by 32 (0 self)
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In 1975, Valiant showed that Boolean matrix multiplication can be used for parsing contextfree grammars (CFGs), yielding the asympotically fastest (although not practical) CFG parsing algorithm known. We prove a dual result: any CFG parser with time complexity $O(g n^{3  \epsilson})$, where $g
Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision
"... The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, ℓ. We prove an upper bound of Õ(n √ ℓ) for all values of ℓ. This is an improvement over previous algorithms for all values of ℓ. On ..."
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Cited by 5 (0 self)
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The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, ℓ. We prove an upper bound of Õ(n √ ℓ) for all values of ℓ. This is an improvement over previous algorithms for all values of ℓ
Fast ContextFree Parsing Requires Fast Boolean Matrix Multiplication
, 1997
"... Valiant showed that Boolean matrix multiplication (BMM) can be used for CFG parsing. We prove a dual result: CFG parsers running in time $O(Gw^{3  \myeps})$ on a grammar $G$ and a string $w$ can be used to multiply $m \times m$ Boolean matrices in time $O(m^{3  \myeps/3})$. In the process we a ..."
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Cited by 3 (0 self)
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Valiant showed that Boolean matrix multiplication (BMM) can be used for CFG parsing. We prove a dual result: CFG parsers running in time $O(Gw^{3  \myeps})$ on a grammar $G$ and a string $w$ can be used to multiply $m \times m$ Boolean matrices in time $O(m^{3  \myeps/3})$. In the process we
Improved OutputSensitive Quantum Algorithms for Boolean Matrix Multiplication
"... We present new quantum algorithms for Boolean Matrix Multiplication in both the time complexity and the query complexity settings. As far as time complexity is concerned, our results show that the product of two n × n Boolean matrices can be computed on a quantum computer in time Õ(n 3/2 + nℓ 3/4), ..."
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Cited by 6 (1 self)
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We present new quantum algorithms for Boolean Matrix Multiplication in both the time complexity and the query complexity settings. As far as time complexity is concerned, our results show that the product of two n × n Boolean matrices can be computed on a quantum computer in time Õ(n 3/2 + nℓ 3
Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions
 Algorithmica
, 1996
"... Small sample spaces with almost independent random variables are applied to design efficient sequential deterministic algorithms for two problems. The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrix multiplication, so ..."
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Cited by 65 (6 self)
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Small sample spaces with almost independent random variables are applied to design efficient sequential deterministic algorithms for two problems. The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrix multiplication
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