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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 03:54, 24 December 2008
, 03:54, 24 December 2008→The Cactus Language : Syntax
Two alternative notations are often useful:
Two alternative notations are often useful:
{| align="center" cellpadding="4" style="text-align:center" width="90%"
|-
| <math>\varepsilon</math>
| =
| <math>^{\backprime\backprime\prime\prime}</math>
| =
| align="left" | the empty string.
|-
| <math>\underline\varepsilon</math>
| =
| <math>\{ \varepsilon \}</math>
| =
| align="left" | the language consisting of a single empty string.
|}
The "kleene star" !A!* of alphabet !A! is the set of all strings over !A!. In particular, !A!* includes among its elements the empty string !e!.
The ''kleene star'' <math>\mathfrak{A}^*</math> of alphabet <math>\mathfrak{A}</math> is the set of all strings over <math>\mathfrak{A}.</math> In particular, <math>\mathfrak{A}^*</math> includes among its elements the empty string <math>\varepsilon.</math>
The "surplus" !A!^+ of an alphabet !A! is the set of all positive length strings over !A!, in other words, everything in !A!* but the empty string.
The "surplus" !A!^+ of an alphabet !A! is the set of all positive length strings over !A!, in other words, everything in !A!* but the empty string.