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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Bibliographic Details
Published in:Algorithms Vol. 10; no. 4; p. 135
Main Authors: Berkemer, Sarah, Höner zu Siederdissen, Christian, Stadler, Peter
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.12.2017
Subjects:
Algebra
Algorithms
Bioinformatics
Domain specific languages
Dynamic programming
Forest management
formal language
Grammars
Parsers
Strings
tree alignment
tree editing
Trees
ISSN:1999-4893, 1999-4893
Online Access:Get full text
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Summary: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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ISSN:1999-4893
1999-4893
DOI:10.3390/a10040135