Normalized Expressions and Finite Automata

There exist two well-known quotients of the position automaton of a regular expression. The first one, called the equation automaton, has first been introduced by Mirkin from the notion of prebase and has been redefined by Antimirov from the notion of partial derivative. The second one, due to Ilie and Yu and called the follow automaton, can be obtained by eliminating ε-transitions in an ε-NFA that is always smaller than the classical ε-NFAs (Thompson, Sippu and Soisalon–Soininen). Ilie and Yu discuss of the difficulty to succeed in a theoretical comparison between the size of the follow automaton and the size of the equation automaton and conclude that it is very likely necessary to realize experimental studies. In this paper we solve the theoretical question, by first defining a set of regular expressions, called normalized expressions and such that every regular expression can be normalized in linear time, and proving then that the equation automaton of a normalized expre...

• Type: Journal
• Year: 2007
• Where: IJAC
• Authors: Jean-Marc Champarnaud, Faissal Ouardi, Djelloul Ziadi
• Keywords: Automaton, Equation Automaton, IJAC 2007, Regular Expression