Algorithms for computing small NFAs

We give new methods for constructing small nondeterministic finite automata (NFA) from regular expressions or from other NFAs. Given an arbitrary NFA, we compute the largest right-invariant equivalence on the states and then merge the states in the same class to obtain a smaller automaton. When applying this method to position automata, we get a way to convert regular expressions into NFAs which can be arbitrarily smaller than the position, partial derivative, and follow automata. In most cases, it is smaller than all NFAs obtained by similar constructions.