Efficient transformations from regular expressions to finite automata

We examine several methods to obtain nondeterministic finite automata without c-transitions (NFA) from regular expressions. The focus is on the size (number of transitions) of the resulting automata, and on the time complexity of the transformation. We show how recent developments [9,6] have improved the size of the resulting automaton from O(n(2)) to O(n(log n)(2)), and even O (n log n) for bounded alphabet size (where n is the size of the regular expression). A lower bound [11] shows this to be close to optimal, and also one of those constructions can be computed in optimal time [8].