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# Parsing Unary Boolean Grammars Using Online Convolution

@inproceedings{Okhotin2010ParsingUB, title={Parsing Unary Boolean Grammars Using Online Convolution}, author={Alexander Okhotin and Christian Reitwie\ssner}, booktitle={Advances and Applications of Automata on Words and Trees}, year={2010} }

- Published 2010 in Advances and Applications of Automata on Words…

Consider context-free grammars generating strings over a one-letter alphabet. For the membership problem for such grammars, stated as “Given a grammar G and a string an, determine whether an is generated by G”, only a näıve O(|G| ·n2)-time algorithm is known. This paper develops a new algorithm solving this problem, which is based upon fast multiplication of integers, works in time |G| · n log n · 2O(log ∗ n), and is applicable to the more general conjunctive and Boolean grammars. The algorithm… CONTINUE READING