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}
}
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

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