Abstract
The problem of outputting all parse trees of a string accepted by a context-free grammar is considered. A systolic algorithms is presented that operates inO(m·n) time, wherem is the number of distinct parse trees andn is the length of the input. The systolic array usesn 2 processors, each of which requires at mostO(logn) bits of storage. This is much more space-efficient that a previously reported systolic algorithm for the same problem, which requiredO(n logn) space per processor. The algorithm also extends previous algorithms that only output a single parse tree of the input.
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Research squpported in part by NSF Grant DCR-8420935 and DCR-8604603.
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Ibarra, O.H., Palis, M.A. An efficient all-parses systolic algorithm for general context-free parsing. Int J Parallel Prog 19, 295–331 (1990). https://doi.org/10.1007/BF01379361
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DOI: https://doi.org/10.1007/BF01379361