Parsing Unary Boolean Grammars Using Online Convolution

Okhotin, Alexander; Reitwießner, Christian

doi:10.4230/DagSemProc.10501.3

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Parsing Unary Boolean Grammars Using Online Convolution

Authors Alexander Okhotin, Christian Reitwießner

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 10501
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2011-05-26

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DOI: 10.4230/DagSemProc.10501.3
URN: urn:nbn:de:0030-drops-31465

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Abstract

In contrast to context-free grammars, the extension of these 
grammars by explicit conjunction, the so-called conjunctive 
grammars can generate (quite complicated) non-regular languages 
over a single-letter alphabet (DLT 2007). Given these 
expressibility results, we study the parsability of Boolean grammars, 
an extension of context-free grammars by conjunction and negation, 
over a unary alphabet and show that they can be parsed in time O(|G| log^2(n) M(n)) 
where M(n) is the time to multiply two n-bit integers. This multiplication 
algorithm is transformed into a convolution algorithm which in turn is 
converted to an online convolution algorithm which is used for the parsing.

Cite As Get BibTex

Alexander Okhotin and Christian Reitwießner. Parsing Unary Boolean Grammars Using Online Convolution. In Advances and Applications of Automata on Words and Trees. Dagstuhl Seminar Proceedings, Volume 10501, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011) https://doi.org/10.4230/DagSemProc.10501.3

Author Details

Alexander Okhotin

Christian Reitwießner

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