Abstract
There is a close relationship between formal language theory and data compression. Since 1990’s various types of grammar-based text compression algorithms have been introduced. Given an input string, a grammar-based text compression algorithm constructs a context-free grammar that only generates the string. An interesting and challenging problem is pattern matching on context-free grammars \(\mathcal{P}\) of size m and \(\mathcal{T}\) of size n, which are the descriptions of pattern string P of length M and text string T of length N, respectively. The goal is to solve the problem in time proportional only to m and n, not to M nor N. Kieffer et al. introduced a very practical grammar-based compression method called multilevel pattern matching code (MPM code). In this paper, we propose an efficient pattern matching algorithm which, given two MPM grammars \(\mathcal{P}\) and \(\mathcal{T}\), performs in O(mn 2) time with O(mn) space. Our algorithm outperforms the previous best one by Miyazaki et al. which requires O(m 2 n 2) time and O(mn) space.
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Inenaga, S., Shinohara, A., Takeda, M. (2004). An Efficient Pattern Matching Algorithm on a Subclass of Context Free Grammars. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_19
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DOI: https://doi.org/10.1007/978-3-540-30550-7_19
Publisher Name: Springer, Berlin, Heidelberg
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