Fast Practical Compression of Deterministic Finite Automata

We revisit the popular delayed deterministic finite automaton (D²FA) compression algorithm introduced by Kumar et al. [SIGCOMM 2006] for compressing deterministic finite automata (DFAs) used in intrusion detection systems. This compression scheme exploits similarities in the outgoing sets of transitions among states to achieve strong compression while maintaining high throughput for matching.
Unfortunately, the D²FA algorithm and later variants of it require at least quadratic compression time since they compare all pairs of states to compute an optimal compression. This is too slow and, in some cases, even infeasible for collections of regular expression in modern intrusion detection systems that produce DFAs of millions of states.
Our main result is a simple, general framework for constructing D²FA based on locality-sensitive hashing that constructs an approximation of the optimal D²FA in near-linear time. We apply our approach to the original D²FA compression algorithm and two important variants, and we experimentally evaluate our algorithms on DFAs from widely used modern intrusion detection systems. Overall, our new algorithms compress up to an order of magnitude faster than existing solutions with either no or little loss of compression size. Consequently, our algorithms are significantly more scalable and can handle larger collections of regular expressions than previous solutions.