Regular expression for a language without empty word. (English) Zbl 0878.68080
Summary: A. Brüggemann-Klein [ibid. 120, No. 2, 197-213 (1993; Zbl 0811.68096)] asks the following question: “Is there a linear-time algorithm transforming a regular expression \(E\) into an expression \(E^-\) with \({\mathcal L}_{E^-}={\mathcal L}_E\backslash\{\varepsilon\}\)?” In this paper, we give a recursive definition of \(E^-\) which enables us to provide such an algorithm. Furthermore, we show that
\[
|E^-|\leq {|E|+1\over 2}\log(|E|+ 1)+ {|E|-1\over 2},
\]
where \(|E|\) is the size of \(E\), and \(|E^-|\) is the size of \(E^-\).
MSC:
68Q45 | Formal languages and automata |
Citations:
Zbl 0811.68096References:
[1] | Brüggemann-Klein, A., Regular expressions into finite automata, Theoret. Comput. Sci., 120, 197-213 (1993) · Zbl 0811.68096 |
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