On NFA Reductions

Lucian Ilie, Gonzalo Navarro, and Sheng Yu

We give faster algorithms for two methods of reducing the number of states in nondeterministic finite automata. The first uses equivalences and the second uses preorders. We develop restricted reduction algorithms that operate on position automata while preserving some of its properties. We show empirically that these reductions are effective in largely reducing the memory requirements of regular expression search algorithms, and compare the effectiveness of different reductions.