Two-Pass Greedy Regular Expression Parsing

We present new algorithms for producing greedy parses for regular expressions (REs) in a semi-streaming fashion. Our lean-log algorithm executes in time O(mn) for REs of size m and input strings of size n and outputs a compact bit-coded parse tree representation. It improves on previous algorithms by: operating in only 2 passes; using only O(m) words of random-access memory (independent of n); requiring only kn bits of sequentially written and read log storage, where k < 1 3 m is the number of alternatives and Kleene stars in the RE; processing the input string as a symbol stream and not requiring it to be stored at all. Previous RE parsing algorithms do not scale linearly with input size, or require substantially more log storage and employ 3 passes where the first consists of reversing the input, or do not or are not known to produce a greedy parse. The performance of our unoptimized C-based prototype indicates that the superior performance of our lean-log algorithm can also be observed in practice; it is also surprisingly competitive with RE tools not performing full parsing, such as Grep.