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A few definitions from formal language theory are required at this point.
 
A few definitions from formal language theory are required at this point.
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An ''alphabet'' is a finite set of signs, typically, !A! = {a_1, ..., a_n}.
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An ''alphabet'' is a finite set of signs, typically, <math>\mathfrak{A} = \{ \mathfrak{a}_1, \ldots, \mathfrak{a}_n \}.</math>
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A ''string'' over an alphabet !A! is a finite sequence of signs from !A!.
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A ''string'' over an alphabet <math>\mathfrak{A}</math> is a finite sequence of signs from <math>\mathfrak{A}.</math>
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The ''length'' of a string is just its length as a sequence of signs. A sequence of length 0 yields the ''empty string'', here presented as "". A sequence of length k > 0 is typically presented in the concatenated forms:
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The ''length'' of a string is just its length as a sequence of signs.
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The ''empty string'' is the unique sequence of length 0.  It is sometimes denoted by an empty pair of quotation marks, <math>^{\backprime\backprime\prime\prime},</math> but more often by the Greek symbols epsilon or lambda.
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A sequence of length <math>k > 0\!</math> is typically presented in the concatenated forms:
    
s_1 s_2 ... s_(k-1) s_k,
 
s_1 s_2 ... s_(k-1) s_k,
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