Parsing by matrix multiplication generalized to Boolean grammars
نویسندگان
چکیده
منابع مشابه
Parsing by matrix multiplication generalized to Boolean grammars
The well-known parsing algorithm for context-free grammars due to Valiant (“General context-free recognition in less than cubic time”, Journal of Computer and System Sciences, 10:2 (1975), 308–314) is analyzed and extended to handle the more general Boolean grammars, which are context-free grammars augmented with conjunction and negation operators in the rules. The algorithm reduces constructio...
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The generalized LR parsing algorithm for context-free grammars is extended for the case of Boolean grammars, which are a generalization of the context-free grammars with logical connectives added to the formalism of rules. In addition to the standard LR operations, Shift and Reduce, the new algorithm uses a third operation called Invalidate, which reverses a previously made reduction. This oper...
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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. how a CFG parser can be used to multiply two Boolean matrices, is presented, which is due to Lee (2002). T...
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Graph data model is widely used in many areas, for example, bioinformatics, graph databases, RDF. One of the most common graph queries are navigational queries. The result of query evaluation are implicit relations between nodes of the graph, i.e. paths in the graph. A natural way to specify these relations is by specifying paths using formal grammars over edge labels. The answer to the context...
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The computational problem of parsing a sentence in a tree-adjoining language is investigated. An interesting relation is studied between this problem and the well-known computational problem of Boolean matrix multiplication: it is shown that any algorithm for the solution of the former problem can easily be converted into an algorithm for the solution of the latter problem. This result bears on...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2014
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2013.09.011