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

Abstract

The follow automaton of a regular expression, recently introduced by Ilie and Yu, is a quotient of the position automaton. The aim of this paper is to present an efficient computation of this quotient, based on specific properties of the ZPC structure of the expression.

Extended to multi-tilde–bar regular expressions and efficient finite automata constructions

“…the size of the expression. The ZPC-structure offers many advantages for efficient constructions of finite automata from regular expressions (follow automaton [9], c-continuation automaton [10], and equation automaton [15]). …”

“…Therefore, all the algorithms based on the ZPC-structure, i.e. the construction of the c-continuation automaton [10], of the equation automaton [10], of the follow automaton [9] and of the weighted position automaton [8] also work for multi-tilde-bar expressions.…”

“…The conversion from a representation into the other one raised numerous research works. Concerning the conversion of a regular expression into a finite automaton we can cite the following references: [1][2][3][4][5][9][10][11]13,14,17,19], for which a common aim is to reduce the space and/or worst case time complexity of the result of the conversion. In this paper we are particularly interested by the implementation of conversion algorithms which are based on the notion of position, such as the five first ones in the above list.…”

“…Our approach is based on a recursive definition of the language associated with an EmtbRE which enlightens the fact that worst case time complexity of the conversion of an EmtbRE into an automaton is related to the worst case time complexity of the computation of the Null function. Finally we show how to extend the ZPC-structure [19] to EmtbREs, which allows us to apply to this family of extended expressions the efficient constructions based on this structure (in particular the construction of the c-continuation automaton [10], the position automaton [19], the follow automaton [9] and the equation automaton [10,15]). …”

Position Automata for Kleene Algebra with Tests

“…Starting from a regular expression r ∈ R(A), we can then obtain a nondeterministic automaton by first marking the symbols, then applying the algorithm above and finally unmarking the labels. If wanted, a deterministic automaton can then be obtained via the subset construction (the complexity of this construction for position automata was studied in [6]).…”