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The problem of outputting all parse trees of a string accepted by a context-free grammar is considered. A systolic algorithm is presented that operates in O (m n) time, where m is the number of distinct parse traces and n is the length of the input. The systolic array uses n2 processors, each of which requires at most O(log n) bits of storage. This is much more space-efficient than a previously reported systolic algorithm for the same problem, which required O (n log n) space per processor. The algorithm also extends previous algorithms that only output a single parse tree of the input.
Oscar H. Ibarra and Michael A. Palis, "An Efficient All-Parses Systolic Algorithm for General Context-Free Parsing", . October 1988.
Date Posted: 05 December 2007