Passage d'une expression rationnelle à un automate fini non-déterministe

FROM THE $\mathcal{ZPC}$ STRUCTURE OF A REGULAR EXPRESSION TO ITS FOLLOW AUTOMATON

“…It can be built in O(|E| 3 ) time by a naive algorithm, and in O(|E| 2 ) time by optimized implementations [2,6,13,15] that manage to compute the set F ollow(F * , x), for all x ∈ Last(F ), as a disjoint union of the sets F ollow(F, x) and F irst(F ). In particular, the solution presented in [2] is based on the notion of SNF.…”

“…The ZPC structure of a regular expression [13,15] is a linear space and time representation of the position automaton that is based on two state forests connected by a set of links. Let us briefly recall how to convert a regular expression into its ZPC structure.…”

“…We create two copies of T (E) denoted by Lasts(E) and F irsts(E), respectively. It has been shown [13,15] …”

“…Let |E| be the size of the expression E, i.e., the number of nodes of its syntax tree and let ||E|| be the number of occurrences of symbols in E. The position automaton of E has ||E|| + 1 states. It can be built in O(|E| 3 ) time by a naive algorithm and in O(|E| 2 ) time by optimized implementations based on expression transformation [2], lazy evaluation [6], or implicit structure computation [13,15].…”

“…More recently, Ilie and Yu [10] have introduced the follow automaton of a regular expression E. There exists an equivalence relation over the set of positions of E, called the follow relation and denoted by ≡ f , such that the follow automaton is the quotient of the position automaton by the relation ≡ f . Our aim is to design an efficient computation of this quotient, based on specific properties of the ZPC structure of the expression [13,15].…”