Changes

A few definitions from formal language theory are required at this point.

A few definitions from formal language theory are required at this point.

An ''alphabet'' is a finite set of signs, typically, !A! = {a_1, ..., a_n}.

An ''alphabet'' is a finite set of signs, typically, <math>\mathfrak{A} = \{ \mathfrak{a}_1, \ldots, \mathfrak{a}_n \}.</math>

A ''string'' over an alphabet !A! is a finite sequence of signs from !A!.

A ''string'' over an alphabet <math>\mathfrak{A}</math> is a finite sequence of signs from <math>\mathfrak{A}.</math>

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:

The ''length'' of a string is just its length as a sequence of signs.

 

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.

 

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,