Implicit Structures to Implement NFA’s from Regular Expressions

Abstract

The aim of this paper is to compare three efficient representations of the position automaton of a regular expression: the Thompson ε-automaton, the ZPC-structure and the F-structure, an optimization of the ZPC-structure. These representations are linear w.r.t. the sizes 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).