Algebraic Dynamic Programming on Trees
Where string grammars describe how to generate and parse strings, tree grammars describe how to generate and parse trees. We show how to extend generalized algebraic dynamic programming to tree grammars. The resulting dynamic programming algorithms are efficient and provide the complete feature set...
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| Vydáno v: | Algorithms Ročník 10; číslo 4; s. 135 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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MDPI AG
01.12.2017
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| ISSN: | 1999-4893, 1999-4893 |
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| Abstract | Where string grammars describe how to generate and parse strings, tree grammars describe how to generate and parse trees. We show how to extend generalized algebraic dynamic programming to tree grammars. The resulting dynamic programming algorithms are efficient and provide the complete feature set available to string grammars, including automatic generation of outside parsers and algebra products for efficient backtracking. The complete parsing infrastructure is available as an embedded domain-specific language in Haskell. In addition to the formal framework, we provide implementations for both tree alignment and tree editing. Both algorithms are in active use in, among others, the area of bioinformatics, where optimization problems on trees are of considerable practical importance. This framework and the accompanying algorithms provide a beneficial starting point for developing complex grammars with tree- and forest-based inputs. |
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| AbstractList | Where string grammars describe how to generate and parse strings, tree grammars describe how to generate and parse trees. We show how to extend generalized algebraic dynamic programming to tree grammars. The resulting dynamic programming algorithms are efficient and provide the complete feature set available to string grammars, including automatic generation of outside parsers and algebra products for efficient backtracking. The complete parsing infrastructure is available as an embedded domain-specific language in Haskell. In addition to the formal framework, we provide implementations for both tree alignment and tree editing. Both algorithms are in active use in, among others, the area of bioinformatics, where optimization problems on trees are of considerable practical importance. This framework and the accompanying algorithms provide a beneficial starting point for developing complex grammars with tree- and forest-based inputs. |
| Author | Höner zu Siederdissen, Christian Stadler, Peter Berkemer, Sarah |
| Author_xml | – sequence: 1 givenname: Sarah surname: Berkemer fullname: Berkemer, Sarah – sequence: 2 givenname: Christian orcidid: 0000-0001-9517-5839 surname: Höner zu Siederdissen fullname: Höner zu Siederdissen, Christian – sequence: 3 givenname: Peter orcidid: 0000-0002-5016-5191 surname: Stadler fullname: Stadler, Peter |
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| Cites_doi | 10.1093/bioinformatics/18.11.1500 10.1093/bioinformatics/btt022 10.1073/pnas.77.11.6309 10.1007/978-1-62703-709-9_12 10.1007/978-3-319-68474-1_11 10.1186/1471-2105-16-S19-S2 10.1093/bioinformatics/btw105 10.1007/BF01734359 10.1016/0020-0190(77)90064-3 10.1016/j.tcs.2016.05.032 10.1007/978-3-642-33122-0_12 10.1006/jagm.2001.1170 10.1017/CBO9780511790492 10.1145/368959.368993 10.1186/1748-7188-5-25 10.1073/pnas.38.8.716 10.1016/0022-2836(70)90057-4 10.1007/978-3-319-38827-4_5 10.1145/1291151.1291199 10.1137/0218082 10.1145/321138.321145 10.3390/a7010062 10.1016/0022-2836(82)90398-9 10.1137/0128004 10.1016/j.tcs.2004.12.030 10.1016/S0304-3975(03)00323-2 10.1145/1863543.1863582 10.1093/bioinformatics/16.8.665 10.1145/1291201.1291211 10.1006/jtbi.1999.1050 10.1145/1291151.1291200 10.1145/2003476.2003484 10.1007/BF00818163 10.1016/0304-3975(95)80029-9 10.1093/sysbio/20.4.406 10.1016/j.is.2015.08.004 10.1007/978-3-642-21458-5_11 10.1109/TCBB.2014.2326155 10.1186/1748-7188-6-26 10.1137/1.9781611975031.77 10.1145/322139.322143 10.1016/S0019-9958(69)90065-5 10.1016/j.scico.2003.12.005 10.1086/656490 10.3233/FI-2014-1054 10.1016/0304-3975(90)90145-8 10.1016/j.scico.2009.11.002 10.2307/2529676 |
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| SubjectTerms | Algebra Algorithms Bioinformatics Domain specific languages Dynamic programming Forest management formal language Grammars Parsers Strings tree alignment tree editing Trees |
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