A parallel algorithm for counting parse trees
A parallel algorithm for computing the number of parse trees of a given string according to a fixed context-free grammar is defined. More generally, the algorithm applies to computing the weight of a string in a weighted grammar over any semiring. The algorithm is first implemented on an arithmetic...
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| Published in: | Information and computation Vol. 303; p. 105237 |
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01.03.2025
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| Abstract | A parallel algorithm for computing the number of parse trees of a given string according to a fixed context-free grammar is defined. More generally, the algorithm applies to computing the weight of a string in a weighted grammar over any semiring. The algorithm is first implemented on an arithmetic circuit of depth at most 6(log2n)2+O(logn) and with O(n6) elements, where the constant factors in the big-O notation depend on the grammar. Then, the circuit is improved using fast matrix multiplication to use only O(n5.38) elements, while preserving depth O((logn)2). |
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| AbstractList | A parallel algorithm for computing the number of parse trees of a given string according to a fixed context-free grammar is defined. More generally, the algorithm applies to computing the weight of a string in a weighted grammar over any semiring. The algorithm is first implemented on an arithmetic circuit of depth at most 6(log2n)2+O(logn) and with O(n6) elements, where the constant factors in the big-O notation depend on the grammar. Then, the circuit is improved using fast matrix multiplication to use only O(n5.38) elements, while preserving depth O((logn)2). |
| ArticleNumber | 105237 |
| Author | Okhotin, Alexander Mikhelson, Margarita |
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| Cites_doi | 10.1016/j.tcs.2013.09.011 10.1016/S0747-7171(08)80013-2 10.1016/j.ic.2020.104672 10.1121/1.2017061 10.1007/BF02165411 10.1016/S0022-0000(75)80046-8 10.1016/0020-0190(88)90164-0 10.1145/2287718.2287719 |
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| Keywords | Weighted grammars Matrix multiplication Parsing Parallel algorithms Context-free grammars |
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| SubjectTerms | Context-free grammars Matrix multiplication Parallel algorithms Parsing Weighted grammars |
| Title | A parallel algorithm for counting parse trees |
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