Abstract
By adding the complement operator (¬), extended regular expressions (ERE) can encode regular languages non-elementarily more succinctly than regular expressions. The ERE membership problem asks whether a word w of size n belongs to the language of an ERE R of size m. Unfortunately, the best known membership algorithms are either non-elementary in m or otherwise require space Ω(n 2) and time Ω(n 3); since in many practical applications n can be very large, these space and time requirements could be prohibitive. In this paper we present an ERE membership algorithm that runs in space O(n ·(logn + m) ·2m) and time O(n 2 ·(logn + m) ·2m). The presented algorithm outperforms the best known algorithms when n is exponentially larger than m.
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Roşu, G. (2007). An Effective Algorithm for the Membership Problem for Extended Regular Expressions. In: Seidl, H. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2007. Lecture Notes in Computer Science, vol 4423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71389-0_24
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DOI: https://doi.org/10.1007/978-3-540-71389-0_24
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