Abstract
A regular expression with n occurrences of symbol can be converted into an equivalent automaton with n + 1 states, the so-called Glushkov automaton of the expression. Conversely, it is possible to decide whether a given (n + 1)-state automaton is a Glushkov one and, if so, to convert it back to an equivalent regular expression of size n. Our goal is to extend the class of automata for which such a linear retranslation is possible. We define new regular operators, called multi-tilde-bars, allowing us to simultaneously apply a multi-tilde operator and a multi-bar one to a list of expressions. The main result is that any acyclic n-state automaton can be turned into an extended expression of size O(n).
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Caron, P., Champarnaud, JM., Mignot, L. (2009). Small Extended Expressions for Acyclic Automata. In: Maneth, S. (eds) Implementation and Application of Automata. CIAA 2009. Lecture Notes in Computer Science, vol 5642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02979-0_23
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DOI: https://doi.org/10.1007/978-3-642-02979-0_23
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