Fast Algorithms for Extended Regular Expression Matching and Searching
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
A fast bit-parallel algorithm for matching extended regular expressions
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
An effective algorithm for the membership problem for extended regular expressions
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
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This paper is concerned with the recognition problem for extended regular expressions: given an extended regular expression r of length m and an input string x of length n, determine if x 驴 L(r), where L(r) denotes the language denoted by r. For this problem, the algorithm based on dynamic programming which runs in O(mn 3) time and O(mn 2) space is widely known. We here introduce a structure called a modular tree and present a new automata-based recognition algorithm such that it runs in O(mn 2 +kn 3) time and O(mn+kn 2) space. Here k is a number derived from a modular tree and is less than the number of intersection and complement operators in r. Furthermore, k can be much smaller than m for many extended regular expressions. Thus our algorithm significantly improves the time and space complexities of the classical dynamic programming algorithm.