Changes

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Each characterization in <math>\mathfrak{K}</math> is an ordered pair of strings <math>(S_1, S_2)\!</math> that takes the following form:

Each characterization in !K! is an ordered pair of strings (S_1, S_2)

that takes the following form:

| S_1 = Q_1 · q · Q_2,

{| align="center" cellpadding="8" width="90%"

|  

| <math>S_1 \ = \ Q_1 \cdot q \cdot Q_2,</math>

| S_2 = Q_1 · W · Q_2.

|-

| <math>S_2 \ = \ Q_1 \cdot W \cdot Q_2.</math>

In this scheme, S_1 and S_2 are members of the augmented strings for !G!,

In this scheme, <math>S_1\!</math> and <math>S_2\!</math> are members of the augmented strings for <math>\mathfrak{G},</math> more precisely, <math>S_1\!</math> is a non-empty string and a sentential form over <math>\mathfrak{G},</math> while <math>S_2\!</math> is a possibly empty string and also a sentential form over <math>\mathfrak{G}.</math>

more precisely, S_1 is a non-empty string and a sentential form over !G!,

while S_2 is a possibly empty string and also a sentential form over !G!.

Here also, q is a non-terminal symbol, that is, q is in {"S"} |_| !Q!,

Here also, <math>q\!</math> is a non-terminal symbol, that is, <math>q \in \{ \, ^{\backprime\backprime} S \, ^{\prime\prime} \, \} \cup \mathfrak{Q},</math> while <math>Q_1, Q_2,\!</math> and <math>W\!</math> are possibly empty strings of non-initial symbols, a fact that can be expressed in the form, <math>Q_1, Q_2, W \in (\mathfrak{Q} \cup \mathfrak{A})^*.</math>

while Q_1, Q_2, and W are possibly empty strings of non-initial symbols,

a fact that can be expressed in the form:  Q_1, Q_2, W in (!Q! |_| !A!)*.

In practice, the ordered pairs of strings in !K! are used to "derive",

In practice, the ordered pairs of strings in !K! are used to "derive",

to "generate", or to "produce" sentences of the language !L! = <!G!>

to "generate", or to "produce" sentences of the language !L! = <!G!>