Computing ε-free NFA from regular expressions in .O(nlog2(n)) time

The standard procedure to transform a regular expression of size n to an epsilon -free nondeterministic finite automaton yields automata with O(n) states and O(n(2)) transitions. For a long time this was supposed to be also the lower bound, but a result by Hromkovic et al. showed how to build an epsilon -free NFA with only O(n log(2)(n)) transitions. The current lower bound on the number of transitions is Omega (n log(n)). A rough running time estimation for the common follow sets (CFS) construction proposed by Hromkovic et al. yields a cubic algorithm. In this paper we present a sequential algorithm for the CFS construction which works in time O(n log(n)+ size of the output). On a CREW PRAM the CFS construction can be performed in time O(log(n)) using O(n + (size of the output)/ log(n)) processors. We also present a simpler proof of the lower bound on the number of transitions.