A parallel algorithm for counting parse trees

A parallel algorithm for computing the number of parse trees of a given string according to a fixed context-free grammar is defined. More generally, the algorithm applies to computing the weight of a string in a weighted grammar over any semiring. The algorithm is first implemented on an arithmetic...

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Bibliographic Details
Published in:	Information and computation Vol. 303; p. 105237
Main Authors:	Mikhelson, Margarita, Okhotin, Alexander
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.03.2025
Subjects:	Context-free grammars Matrix multiplication Parallel algorithms Parsing Weighted grammars Weighted grammars Matrix multiplication Parsing Parallel algorithms Context-free grammars
ISSN:	0890-5401
Online Access:	Get full text
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Summary:	A parallel algorithm for computing the number of parse trees of a given string according to a fixed context-free grammar is defined. More generally, the algorithm applies to computing the weight of a string in a weighted grammar over any semiring. The algorithm is first implemented on an arithmetic circuit of depth at most 6(log2⁡n)2+O(log⁡n) and with O(n6) elements, where the constant factors in the big-O notation depend on the grammar. Then, the circuit is improved using fast matrix multiplication to use only O(n5.38) elements, while preserving depth O((log⁡n)2).
ISSN:	0890-5401
DOI:	10.1016/j.ic.2024.105237