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On the complexity of general context-free language parsing and recognition

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Automata, Languages and Programming (ICALP 1979)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 71))

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Several results on the computational complexity of general context-free language parsing and recognition are given. In particular we show that parsing strings of length n is harder than recognizing such strings by a factor of only 0(log n), at most. The same is true for linear and/or unambiguous context-free languages. We also show that the time to multiply \(\sqrt n \times \sqrt n\) Boolean Matrices is a lower bound on the time to recognize all prefixes of a string (or do on-line recognition), which in turn is a lower bound on the time to generate a particular convenient representation of all parses of a string (in an ambiguous grammar). Thus these problems are solvable in linear time only if n×n Boolean matrix multiplication can be done in 0(n2).

This research supported by an IBM pre-doctoral fellowship and by NSF grants GJ-474 and MCS77-02474.

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Hermann A. Maurer

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© 1979 Springer-Verlag Berlin Heidelberg

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Ruzzo, W.L. (1979). On the complexity of general context-free language parsing and recognition. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-540-09510-1

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