New Algorithms for Regular Expression Matching

In this paper we revisit the classical regular expression matching problem, namely, given a regular expression R and a string Q, decide if Q matches one of the strings specified by R. Let m and n be the length of R and Q, respectively. On a standard unit-cost RAM with word length w ≥ log n, we show that the problem can be solved in O(m) space with the following running times:    O(nm log w w + m logw) if m > w O(n logm + m logm) if √ w < m ≤ w O(min(n + m, n logm + m logm)) if m ≤ √ w. This improves the best known time bound among algorithms using O(m) space. Whenever w ≥ log n it improves all known time bounds regardless of how much space is used.