Abstract
The standard procedure to transform a regular expression of size n to an ϵ -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 ϵ -free NFA with only O ( n log 2 ( n )) transitions. The current lower bound on the number of transitions is Ω( 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.
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