MyWikiBiz, Author Your Legacy — Friday April 04, 2025
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334 bytes added
, 03:54, 24 December 2008
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Two alternative notations are often useful:
Two alternative notations are often useful:
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# !e! = @e@ = "" = the empty string.
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{| align="center" cellpadding="4" style="text-align:center" width="90%"
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# %e% = {!e!} = {""} = the language consisting of a single empty string.
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|-
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| <math>\varepsilon</math>
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| =
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| <math>^{\backprime\backprime\prime\prime}</math>
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| =
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| align="left" | the empty string.
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|-
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| <math>\underline\varepsilon</math>
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| =
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| <math>\{ \varepsilon \}</math>
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| =
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| align="left" | the language consisting of a single empty string.
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|}
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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!.
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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.