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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| Vydáno v: | Information and computation Ročník 303; s. 105237 |
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| Jazyk: | angličtina |
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01.03.2025
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| ISSN: | 0890-5401 |
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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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| References | Lafferty (br0080) 2000 Rytter (br0100) 1984; vol. 208 Brent, Goldschlager (br0040) 1984; 6 Bakinova, Basharin, Batmanov, Lyubort, Okhotin, Sazhneva (br0020) 2022; 283 Gazit, Miller (br0060) 1988; 28 Coppersmith, Winograd (br0050) 1990; 9 Valiant (br0130) 1975; 10 Vassilevska Williams, Xu, Xu, Zhou (br0140) 2024 Wegener (br0150) 1987 Baker (br0010) 1979; 65 Okhotin (br0090) 2014; 516 Gelade, Marquardt, Schwentick (br0070) 2012; 13 Volker (br0120) 1969; 13 Benedí, Sánchez (br0030) 2007; vol. 4477 Schmidt, Schwentick, Todtenhoefer (br0110) 2023; vol. 272 Vassilevska Williams (10.1016/j.ic.2024.105237_br0140) 2024 Coppersmith (10.1016/j.ic.2024.105237_br0050) 1990; 9 Schmidt (10.1016/j.ic.2024.105237_br0110) 2023; vol. 272 Benedí (10.1016/j.ic.2024.105237_br0030) 2007; vol. 4477 Lafferty (10.1016/j.ic.2024.105237_br0080) 2000 Rytter (10.1016/j.ic.2024.105237_br0100) 1984; vol. 208 Gelade (10.1016/j.ic.2024.105237_br0070) 2012; 13 Volker (10.1016/j.ic.2024.105237_br0120) 1969; 13 Brent (10.1016/j.ic.2024.105237_br0040) 1984; 6 Bakinova (10.1016/j.ic.2024.105237_br0020) 2022; 283 Gazit (10.1016/j.ic.2024.105237_br0060) 1988; 28 Wegener (10.1016/j.ic.2024.105237_br0150) 1987 Okhotin (10.1016/j.ic.2024.105237_br0090) 2014; 516 Valiant (10.1016/j.ic.2024.105237_br0130) 1975; 10 Baker (10.1016/j.ic.2024.105237_br0010) 1979; 65 |
| References_xml | – volume: 6 year: 1984 ident: br0040 article-title: A parallel algorithm for context-free parsing publication-title: Aust. Comput. Sci. Commun. – volume: 13 start-page: 354 year: 1969 end-page: 356 ident: br0120 article-title: Gaussian elimination is not optimal publication-title: Numer. 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| Title | A parallel algorithm for counting parse trees |
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