Regular expression matching asks whether a string of length $n$ belongs to the language described by a regular expression of length $m$. We give an algorithm that solves this problem in linear space and $O(nm \log \log n/\log^2 n + n + m)$ time. This improves the leading term of the previous best worst-case constant-alphabet time bound by a factor of $\sqrt{\log n}$. The key new technique is a two-dimensional tabulation specialized to the regular expression.

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