Evaluation of Three Implicit Structures to Implement Nondeterministic Automata From Regular Expressions

The aim of this paper is to compare three efficient representations of the position automaton of a regular expression: the Thompson εautomaton, the ZPC-structure and the F-structure, an optimization of the ZPC-structure. These representations are linear w.r.t. the size s of the expression, since their construction is in O(s) space and time, as well as the computation of the set δ(X, a) of the targets of the transitions by a of any subset X of states. The comparison is based on the evaluation of the number of edges of the underlying graphs respectively created by the construction step or visited by the computation of a set δ(X,a).