EVALUATION OF THREE IMPLICIT STRUCTURES TO IMPLEMENT NONDETERMINISTIC AUTOMATA 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 ∊-automaton, the [Formula: see text]-structure and the ℱ-structure, an optimization of the [Formula: see text]-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).