Computing ε-free NFA from regular expressions in O(n log2(N)) time
The standard procedure to transform a regular expression to an ε-free NFA yields a quadratic blow-up of the number of transitions. For a long time this was viewed as an unavoidable fact. Recently Hromkovič et.al.  exhibited a construction yielding ε-free NFA with O(n log2(n)) transitions. A rough estimation of the time needed for their construction shows a cubic time bound. The known lower bound is Ω(n log(n)). In this paper we present a sequential algorithm for the construction described in  which works in time O(n log(n) + size of the output). On a CREW PRAM the construction is possible in time O(log(n)) using O(n + (size of the output)/log(n)) processors.
Unable to display preview. Download preview PDF.
- 4.A. Gibbons and W. Rytter. Efficient Parallel Algorithms. Cambridge University Press, 1989.Google Scholar
- 5.J. Hromkovič, S. Seibert, and T. Wilke. Translating regular expressions into small ε-free nondeterministic finite automata. In Proc. of the 14th Ann. Symp. on Theor. Aspects of Comp. Sci. (STACS'97), no. 1200 in LNCS, p. 55–66, 1997. Springer.Google Scholar