Corrigendum to our paper: How Expressions Can Code for Automata

In a previous paper, we have described the construction of an automaton from a rational expression which has the property that the automaton built from an expression which is itself computed from a co-deterministic automaton by the state elimination method is co-deterministic. It turned out that the definition on which the construction is based was inappropriate, and thus the proof of the property was flawed. We give here the correct definition of the broken derived terms of an expression which allow to define the automaton and the detailed full proof of the property. 1991 Mathematics Subject Classification. 68Q45, 68Q70. 1. The problem, its partial solution, and a flaw The conversion of finite automata into regular expressions and conversely of regular expressions to finite automata is an old, and fundamental, problem in automata theory. The algorithms that produce an expression which denotes the language accepted by a finite automaton (McNaugton–Yamada algorithm, state elimination method) are more or less ‘equivalent’ [9] and yield an expression whose length may be exponential in the size of the automaton. The algorithms that build a (non deterministic) automaton from an expression (Glushkov, Antimirov) output an automaton whose size is roughly (and at most for Antimirov) equal to the length of the expression. In a previous paper of ours [8], we have considered the possibility of finding a method that would be reversible, in the sense that